Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68228120170401Quadratic $alpha$-functional equations19235110.22075/ijnaa.2017.1066.1218ENChoonkilParkResearch nstitute for natural sciences,
Hanyang University Seoul 04763,
KoreaSang OgKimDepartment of Mathematics
Hallym University
Chuncheon 24252
KoreaJournal Article20151218In this paper, we solve the quadratic $alpha$-functional equations $2f(x) + 2f(y) = f(x + y) + alpha^{-2}f(alpha(x-y)); (0.1)$ where $alpha$ is a fixed non-Archimedean number with $alpha^{-2}neq 3$. Using the fixed point method and the direct method, we prove the Hyers-Ulam stability of the quadratic $alpha$-functional equation (0.1) in non-Archimedean Banach spaces.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68228120170401The operators over the GIFS1121240210.22075/ijnaa.2017.11099.1542ENEzzatallahBaloui JamkhanehDepartment of Statistics, Qaemshahr Branch, Islamic Azad University, Qaemshahr, IranJournal Article20160222In this paper, newly defined level operators and modal-like operators over extensional generalized intuitionistic fuzzy sets (GIFSB) are proposed. Some of the basic properties of the new operators are discussed.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68228120170430On genuine Lupac{s}-Beta operators and modulus of continuity2332230710.22075/ijnaa.2017.10557.1508ENVijayGuptaNetaji Subhas Institute of Technology
New Delhi, IndiaTh.M.RassiasDepartment of Mathematics, National Technical University of Athens, Zofrafou Campus, 15780 Athens, GreeceEktaPandeyDepartment of Mathematics, IMS Engineering College Ghaziabad-201009, (UP), IndiaJournal Article20160414In the present article we discuss approximation properties of genuine Lupac{s}-Beta operators of integral type. We establish quantitative asymptotic formulae and a direct estimate in terms of Ditzian-Totik modulus of continuity. Finally we mention results on the weighted modulus of continuity for the genuine operators.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68228120170505Stability for certain subclasses of harmonic univalent functions3345240510.22075/ijnaa.2017.2405ENAliEbadianDepartment of Mathematics, Payame Noor University, P.O. BOX 19395-3697, Tehran, IranSamanAziziDepartment of Mathematics, Payame Noor University, P.O. BOX 19395-3697, Tehran, IranShahramNajafzadehDepartment of Mathematics, Payame Noor University, P.O. BOX 19395-3697, Tehran, IranJournal Article20160112In this paper, the problem of stability for certain subclasses of harmonic univalent functions is investigated. Some lower bounds for the radius of stability of these subclasses are found.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68228120170401Hermite-Hadamard inequality for geometrically quasiconvex functions on co-ordinates476048310.22075/ijnaa.2016.483ENAliBaraniDepartment of Mathematics, Lorestan University, P. O. Box 465, Khoramabad, IranFatemehMalmirDepartment of Mathematics, Lorestan University, P. O. Box 465, Khoramabad, IranJournal Article20150427In this paper we introduce the concept of geometrically quasiconvex functions on the co-ordinates and establish some Hermite-Hadamard type integral inequalities for functions defined on rectangles in the plane. Some inequalities for product of two geometrically quasiconvex functions on the co-ordinates are considered.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68228120170401Study on efficiency of the Adomian decomposition method for stochastic differential equations616848410.22075/ijnaa.2016.484ENKazemNouriDepartment of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, Semnan 35195-363, IranJournal Article20150311Many time-varying phenomena of various fields in science and engineering can be modeled as a stochastic differential equations, so investigation of conditions for existence of solution and obtain the analytical and numerical solutions of them are important. In this paper, the Adomian decomposition method for solution of the stochastic differential equations are improved. Uniqueness and convergence of their adapted solutions are reviewed. The efficiency of the method is demonstrated through the two numerical experiments.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68228120170605A spline collocation method for integrating a class of chemical reactor equations6980249510.22075/ijnaa.2017.1653.1436ENAbdelmajidElhajajiENCG El JadidaNadiaBarjeLMC Laboratory, FST, University of Sultan Moulay Slimane, Beni-Mellal, MoroccoAbdelhafidSerghiniMATSI Laboratory, ESTO, University Mohammed Premier, Oujda, MoroccoKhalidHilalLMC Laboratory, FST, University of Sultan Moulay Slimane, Beni-Mellal, MoroccoEl BekkayeMermriDepartment of Mathematics and Computer Science, FS, University Mohammed Premier, Oujda, MoroccoJournal Article20161010. In this paper, we develop a quadratic spline collocation method for integrating the nonlinear partial differential equations (PDEs) of a plug flow reactor model. The method is proposed in order to be used for the operation of control design and/or numerical simulations. We first present the Crank-Nicolson method to temporally discretize the state variable. Then, we develop and analyze the proposed spline collocation method for the spatial discretization. The design of the collocation method is interpreted as one order error convergent. This scheme is applied on some test examples, the numerical results illustrate the efficiency of the method and confirm the theoretical behavior of the rates of convergence.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68228120170410Uncertainty in linear fractional transportation problem819350410.22075/ijnaa.2016.504ENMohammad RezaSafiDepartment of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, Semnan 35195-363, IranSeyyed MojtabaGhasemiDepartment of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, Semnan 35195-363, IranJournal Article20151228In this paper, we study the linear fractional transportation problem with uncertain arameters. After recalling some definitions, concepts and theorems in uncertainty theory we present three approaches for solving this problem. First we consider the expected value of the objective function together with the expectation of satisfying constraints. Optimizing the expected value of the objective function with considering chance constrained method for the restrictions is our second approach. In the third approach we add the objective function to the constraints and solve again the problem by chance constrained method. A numerical example is solved by three approaches and their solutions are compaired.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68228120170605Dhage iteration method for PBVPs of nonlinear first order hybrid integro-differential equations95112234910.22075/ijnaa.2017.997.1194ENBapuraoDhageKasubai, Gurukul Colony, Ahmedpur-413 515, Dist: Latur, Maharashtra, IndiaJournal Article20151113In this paper, author proves the algorithms for the existence as well as the approximation of solutions to a couple of periodic boundary value problems of nonlinear first order ordinary integro-differential equations using operator theoretic techniques in a partially ordered metric space. The main results rely on the Dhage iteration method embodied in the recent hybrid fixed point theorems of Dhage in a partially ordered normed linear space. The approximation of the solutions are obtained under weaker mixed partial continuity and partial Lipschitz conditions. Our hypotheses and abstract results are also illustrated by some numerical examples.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68228120170605The James and von Neumann-Jordan type constants and uniform normal structure in Banach spaces113122234810.22075/ijnaa.2017.2348ENMinaDinarvandFaculty of Mathematics, K. N. Toosi University of Technology, Tehran, IranJournal Article20150316Recently, Takahashi has introduced the James and von Neumann-Jordan type constants. In this paper, we present some sufficient conditions for uniform normal structure and therefore the fixed point property of a Banach space in terms of the James and von Neumann-Jordan type constants and the Ptolemy constant. Our main results of the paper significantly generalize and improve many known results in the recent literature.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68228120170606Convergence of trajectories in infinite horizon optimization123131249610.22075/ijnaa.2017.1326.1327ENSaraHassaniFederation university of AustraliaMusaMammadovFederation university of AustraliaJournal Article20160414In this paper, we investigate the convergence of a sequence of minimizing trajectories in infinite horizon optimization problems. The convergence is considered in the sense of ideals and their particular case called the statistical convergence. The optimality is defined as a total cost over the infinite horizon.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68228120170401Some results on coupled fixed point and fixed point theory in partially ordered probabilistic like (quasi) Menger spaces133157235010.22075/ijnaa.2017.1064.1215ENHamidShayanpourFaculty of Mathematical Sciences, Department of Pure Mathematics,
University of Shahrekord, P. O. Box 88186-34141, Shahrekord, Iran.AsiyehNematizadehFaculty of Mathematical Sciences, Department of Pure Mathematics, University
of Shahrekord, P. O. Box 88186-34141, Shahrekord, Iran.Journal Article20151217In this paper, we define the concept of probabilistic like Menger (probabilistic like quasi Menger) space (briefly, PLM-space (PLqM-space)). We present some coupled fixed point and fixed point results for certain contraction type maps in partially order PLM-spaces (PLqM- spaces).Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68228120170401On the metric triangle inequality159164249710.22075/ijnaa.2017.1602.1418ENAlexandreMihai BicaDepartment of Mathematics and Informatics, University of Oradea, Universitatii Street no. 1, 410087 Oradea, RomaniaJournal Article20160914A non-contradictible axiomatic theory is constructed under the local reversibility of the metric triangle inequality. The obtained notion includes the metric spaces as particular cases and the generated metric topology is T$_{1}$-separated and generally, non-Hausdorff.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68228120170401Existence results for equilibrium problems under strong sign property165176249810.22075/ijnaa.2017.2498ENSomayeJafariDepartment of Mathematics, Razi University, KermanshahAliFarajzadehDepartment of Mathematics, Razi University, KermanshahJournal Article20150704This paper concerns equilibrium problems in real metric linear spaces. Considering a modified notion of upper sign property for bifunctions, we obtain the relationship between the solution sets of the local Minty equilibrium problem and the equilibrium problem, where the technical conditions on $f$ used in the literature are relaxed. The KKM technique is used to generalize and unify some existence results for the relaxed $mu$-quasimonotone equilibrium problems in the literature.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68228120170606Unsteady free convection oscillatory couette flow through a variable porous medium with concentration profile177186249910.22075/ijnaa.2017.672.1107ENSurjanSinghDST-CIMS BHU VaranasiPawanKumar SharmaAmity School Of Engineering And Technology, 580, Delhi Palam Vihar Road, Bijwasan, New Delhi 110061, IndiaKavindraNath RaiIIT BHU, VaranasiNagendraSingh TomerGovernment College Hisar HaryanaJournal Article20150116In this paper we have studied the effect of free convection on the heat transfer and flow through variable porous medium which is bounded by two vertical parallel porous plates. In this study it is assume that free stream velocity oscillates with time about a constant mean. Periodic temperature is considered in the moving plate. Effect of different parameters on mean flow velocity, Transient velocity, Concentration profile and transient temperature studied in detail.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68228120170606Almost n-Multiplicative Maps between Frechet Algebras187195250010.22075/ijnaa.2017.2500ENTaherGhasemi HonaryDepartment of Mathematics, Kharazmi University, Tehran, IranMashaalahOmidiDepartment of Basic Sciences, Kermanshah University of Technology, Kermanshah, IranAmirHosseinSanatpourDepartment of Mathematics, Kharazmi University, Tehran, IranJournal Article20160522For the Fr'{e}chet algebras $(A, (p_k))$ and $(B, (q_k))$ and $n in mathbb{N}$, $ngeq 2$, a linear map $T:A rightarrow B$ is called textit{almost $n$-multiplicative}, with respect to $(p_k)$ and $(q_k)$, if there exists $varepsilongeq 0$ such that<br />$$q_k(Ta_1a_2cdots a_n-Ta_1Ta_2cdots Ta_n)leq varepsilon p_k(a_1) p_k(a_2)cdots p_k(a_n),$$<br />for each $kin mathbb{N}$ and $a_1, a_2, ldots, a_nin A$. The linear map $T$ is called textit{weakly almost $n$-multiplicative}, if there exists $varepsilongeq 0$ such that for every $kin mathbb{N}$ there exists $n(k)in mathbb{N}$ with<br />$$q_k(Ta_1a_2cdots a_n-Ta_1Ta_2cdots Ta_n)leq varepsilon p_{n(k)}(a_1) p_{n(k)}(a_2)cdots p_{n(k)}(a_n),$$<br />for each $k in mathbb{N}$ and $a_1, a_2, ldots, a_nin A$.<br />The linear map $T$ is called $n$-multiplicative if<br />$$Ta_{1}a_{2} cdots a_{n} = Ta_{1} Ta_{2} cdots Ta_{n},$$<br />for every $a_{1}, a_{2},ldots, a_{n} in A$.<br /><br />In this paper, we investigate automatic continuity of (weakly) almost $n$-multiplicative maps between certain classes of Fr'{e}chet algebras, including Banach algebras. We show that if $(A, (p_k))$ is a Fr'{e}chet algebra and $T: A rightarrow mathbb{C}$ is a weakly almost $n$-multiplicative linear functional, then either $T$ is $n$-multiplicative, or it is continuous. Moreover, if $(A, (p_k))$ and $(B, (q_k))$ are Fr'{e}chet algebras and $T:A rightarrow B$ is a continuous linear map, then under certain conditions $T$ is weakly almost $n$-multiplicative for each $ngeq 2$. In particular, every continuous linear functional on $A$ is weakly almost $n$-multiplicative for each $ngeq 2$.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68228120170624On the real quadratic fields with certain continued fraction expansions and fundamental units197208257010.22075/ijnaa.2017.1610.1420ENOzenOzerDepartment of Mathematics, Faculty of Science and Arts, Ki rklareli University, 39000-Ki rklareli, TurkeyAhmedKhammashDepartment of Mathematics, Al-Qura University, Makkah,21955, Saudi ArabiaJournal Article20160917The purpose of this paper is to investigate the real quadratic number fields $Q(sqrt{d})$ which contain the specific form of the continued fractions expansions of integral basis element where $dequiv 2,3( mod 4)$ is a square free positive integer. Besides, the present paper deals with determining the fundamental unit<br />$$epsilon _{d}=left(t_d+u_dsqrt{d}right) 2left.right > 1$$<br />and $n_d$ and $m_d$ Yokoi's $d$-invariants by reference to continued fraction expansion of integral basis element where $ell left({d}right)$ is a period length. Moreover, we mention class number for such fields. Also, we give some numerical results concluded in the tables.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68228120170606$C$-class and $F(psi,varphi)$-contractions on $M$-metric spaces209224250210.22075/ijnaa.2017.1636.1429ENHosseinMonfaredDepartment of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, IranMahdiAzhiniDepartment of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, IranMehdiAsadiDepartment of Mathematics, Zanjan Branch, Islamic Azad University, Zanjan, IranJournal Article20160928Partial metric spaces were introduced by Matthews in 1994 as a part of the study of denotational semantics of data flow networks. In 2014 Asadi and {it et al.} [New Extension of $p$-Metric Spaces with Some fixed point Results on $M$-metric paces, J. Ineq. Appl. 2014 (2014): 18] extend the Partial metric spaces to $M$-metric spaces. In this work, we introduce the class of $F(psi,varphi)$-contractions and investigate the existence and uniqueness of fixed points for the new class $mathcal{C}$ in the setting of $M$-metric spaces. The theorems that we prove generalize many previously obtained results. We also give some examples showing that our theorems are indeed proper extensions.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68228120170401Hermite-Hadamard inequalities for $mathbb{B}$-convex and $mathbb{B}^{-1}$-convex functions225233250310.22075/ijnaa.2017.1621.1427ENIlknurYesilceMersin University, Faculty of Science and Letters, Department of Mathematics, 33343, Mersin, TurkeyGabilAdilovAkdeniz University, Faculty of Education, Department of Mathematics, 07058, Antalya, TurkeyJournal Article20160926Hermite-Hadamard inequality is one of the fundamental applications of convex functions in Theory of Inequality. In this paper, Hermite-Hadamard inequalities for $mathbb{B}$-convex and $mathbb{B}^{-1}$-convex functions are proven.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68228120170607Some properties of analytic functions related with bounded positive real part235244239710.22075/ijnaa.2017.1154.1308ENRahimKargarYoung Researchers and Elite Club, Urmia Branch, Islamic Azad University, Urmia, IranAliEbadianDepartment of Mathematics, Payame Noor University, IranJanuszSokolDepartment of Mathematics, Rzeszow University of Technology, Al. Powstancow Warszawy 12, 35-959 Rzeszow, PolandJournal Article20160314In this paper, we define new subclass of analytic functions related with bounded positive real part, and coefficients estimates, duality and neighborhood are considered.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68228120170608Strong and $Delta$-convergence theorems for total asymptotically nonexpansive mappings in CAT(0)245260250410.22075/ijnaa.2017.2504ENG.S.SalujaDepartment of Mathematics, Govt. Nagarjuna P.G. College of Science, Raipur - 492010 (C.G.), IndiaHemant KumarNashineDepartment of Mathematics, Texas A & M University - Kingsville - 78363-8202, Texas, USA0000-0002-0250-9172Yumnam RohenSinghNational Institute of Technology Manipur, Takyelpat, Imphal-795001, Manipur, IndiaJournal Article20150725In this work we use the Noor iteration process for total asymptotically nonexpansive mapping to establish the strong and $Delta$-convergence theorems in the framework of CAT(0) spaces. By doing this, some of the results existing in the current literature generalize, unify and extend.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68228120170611A note on the Young type inequalities261267250610.22075/ijnaa.2017.1231.1289ENLeilaNasiriDepartment Mathematics, Lorestan University, IranMahmoodShakooriDepartment Mathematics, Lorestan University, IranWenshiLiaoCollege of Mathematics and Statistics, Chongqing University, Chongqing, 401331, P.R. ChinaJournal Article20160224In this paper, we present some refinements of the famous Young type inequality. As application of our result, we obtain some matrix inequalities for the Hilbert-Schmidt norm and the trace norm. The results obtained in this paper can be viewed as refinement of the derived results by H. Kai [Young type inequalities for matrices, J. East China Norm. Univ. 4 (2012) 12--17].Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68228120170401An inexact alternating direction method with SQP regularization for the structured variational inequalities269289250910.22075/ijnaa.2017.1860.1485ENAbdellahBnouhachemIbn Zohr University, ENSA, BP 1136, Agadir, MoroccoTh.M.RassiasDepartment of Mathematics, National Technical University of Athens, Zofrafou Campus, 15780 Athens, GreeceJournal Article20161110In this paper, we propose an inexact alternating direction method with square quadratic proximal (SQP) regularization for the structured variational inequalities. The predictor is obtained via solving SQP system approximately under significantly relaxed accuracy criterion and the new iterate is computed directly by an explicit formula derived from the original SQP method. Under appropriate conditions, the global convergence of the proposed method is proved. We show the $O(1/t)$ convergence rate for the inexact SQP alternating direction method. We also reported some numerical results to illustrate the efficiency of the proposed method.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68228120170612Similarity measurement for describe user images in social media291299251010.22075/ijnaa.2017.10744.1522ENAlirezaTavakoli TarghiCS group of Mathematics department, Shahid Beheshti University, Tehran, IranJournal Article20160213Online social networks like Instagram are places for communication. Also, these media produce rich metadata which are useful for further analysis in many fields including health and cognitive science. Many researchers are using these metadata like hashtags, images, etc. to detect patterns of user activities. However, there are several serious ambiguities like how much reliable are these information. In this paper, we attempt to answer two main questions. Firstly, are image hashtags directly related to image concepts? Can image concepts being predicted using machine learning models? The results of our analysis based on 105000 images on Instagram show that user hashtags are hardly related to image concepts (only 10%of test cases). Second contribution of this paper is showing the suggested pre-trained model predicate image concepts much better (more than 50% of test cases) than user hashtags. Therefore, it is strongly recommended to social media researchers not to rely only on the user hashtags as a label of images or as a signal of information for their study. Alternatively, they can use machine learning methods line deep convolutional neural network model to describe images to extract more related contents. As a proof of concept, some results on food images are studied. We use few similarity measurements to compare result of human and deep convolutional neural network. These analysis is important because food is an important society health field.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68228120170612Periodic boundary value problems for controlled nonlinear impulsive evolution equations on Banach spaces301314251110.22075/ijnaa.2017.1460.1370ENSaidMellianiDepartment of Mathematics, Faculty of Sciences and Technics, Sultan Moulay Slimane University, BP 523 Beni Mellal 23000, MoroccoLalla SaadiaChadliDepartment of Mathematics, Faculty of Sciences and Technics, Sultan Moulay Slimane University, BP 523 Beni Mellal 23000, MoroccoAbdelatiEl AllaouiDepartment of Mathematics, Faculty of Sciences and Technics, Sultan Moulay Slimane University, BP 523 Beni Mellal 23000, Morocco0000-0001-7197-4951Journal Article20160619This paper deals with the Periodic boundary value problems for Controlled nonlinear impulsive evolution equations. By using the theory of semigroup and fixed point methods, some conditions ensuring the existence and uniqueness. Finally, two examples are provided to demonstrate the effectiveness of the proposed results.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68228120170612Fixed and coincidence points for hybrid rational Geraghty contractive mappings in ordered $b$-metric spaces31532945310.22075/ijnaa.2016.453ENArsalanAnsariDepartment of Mathematics, Karaj Branch, Islamic Azad University, Karaj, IranAbdolrahmanRazaniDepartment of Mathematics, Faculty of Science, Imam Khomeini International University, Postal code 34149-16818, Qazvin, IranNawabHussainDepartment of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaJournal Article20151105In this paper, we present some fixed and coincidence point theorems for hybrid rational Geraghty contractive mappings in partially ordered $b$-metric spaces. Also, we derive certain coincidence point results for such contractions. An illustrative example is provided here to highlight our findings.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68228120170613New integral inequalities for $s$-preinvex functions331336251310.22075/ijnaa.2017.3084.1498ENBadreddineMeftahLaboratoire des t\'{e}l\'{e}communications, Facult\'{e} des Sciences et de la Technologie, University of 8 May 1945 Guelma, P.O. Box 401, 24000 Guelma, AlgeriaJournal Article20170125In this note, we give some estimate of the generalized quadrature formula of Gauss-Jacobi<br />$$underset{a}{overset{a+eta left( b,aright) }{int }}left( x-aright)^{p}left( a+eta left( b,aright) -xright) ^{q}fleft( xright) dx$$<br />in the cases where $f$ and $left| fright| ^{lambda }$ for $lambda >1$, are $s$-preinvex functions in the second sense.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68228120170613Some extensions of Darbo's theorem and solutions of integral equations of Hammerstein type337351251610.22075/ijnaa.2017.1355.1334ENRezaAllahyariDepartment of Mathematics, Mashhad Branch, Islamic Azad University,mashhad, IranAsadollahAghajaniSchool of Mathematics, Iran University of Science and Technology, Narmark, Tehran 16846 13114, IranJournal Article20160425In this brief note, using the technique of measures of noncompactness, we give some extensions of Darbo fixed point theorem. Also we prove an existence result for a quadratic integral equation of Hammerstein type on an unbounded interval in two variables which includes several classes of nonlinear integral equations of Hammerstein type. Furthermore, an example is presented to show the efficiency of our result.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68228120170613On new faster fixed point iterative schemes for contraction operators and comparison of their rate of convergence in convex metric spaces353388252310.22075/ijnaa.2017.11144.1543ENCristianAlecsaBabe\c s-Bolyai University, Department of Mathematics, Cluj-Napoca, Romania, Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy, Cluj-Napoca, RomaniaJournal Article20170425In this paper we present new iterative algorithms in convex metric spaces. We show that these iterative schemes are convergent to the fixed point of a single-valued contraction operator. Then we make the comparison of their rate of convergence. Additionally, numerical examples for these iteration processes are given.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68228120170401The structure of ideals, point derivations, amenability and weak amenability of extended Lipschitz algebras38940449310.22075/ijnaa.2016.493ENMalihehMayghaniDepartment of Mathematics, Payame Noor University, Tehran, 19359-3697, IranDavoodAlimohammadiDepartment of Mathematics, Faculty of Science, Arak University,
Arak, IranJournal Article20160317Let $(X,d)$ be a compact<br />metric space and let $K$ be a nonempty compact subset of $X$. Let $alpha in (0, 1]$ and let ${rm Lip}(X,K,d^ alpha)$ denote the Banach algebra of all continuous complex-valued functions $f$ on<br />$X$ for which<br />$$p_{(K,d^alpha)}(f)=sup{frac{|f(x)-f(y)|}{d^alpha(x,y)} : x,yin K , xneq y}<infty$$<br />when it is equipped with the algebra norm $||f||_{{rm Lip}(X, K, d^ {alpha})}= ||f||_X+ p_{(K,d^{alpha})}(f)$, where $||f||_X=sup{|f(x)|:~xin X }$. In this paper we first study the structure of certain ideals of ${rm Lip}(X,K,d^alpha)$. Next we show that if $K$ is infinite and ${rm int}(K)$ contains a limit point of $K$ then ${rm Lip}(X,K,d^alpha)$ has at least a nonzero continuous point derivation and applying this fact we prove that ${rm Lip}(X,K,d^alpha)$ is not weakly amenable and amenable.