2020-07-12T15:11:54Z
https://ijnaa.semnan.ac.ir/?_action=export&rf=summon&issue=318
International Journal of Nonlinear Analysis and Applications
IJNAA
2017
8
1
Quadratic $alpha$-functional equations
Choonkil
Park
Sang Og
Kim
In 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.
Hyers-Ulam stability
non-Archimedean normed space
direct method
Fixed point
quadratic $alpha$-functional equation
2017
04
01
1
9
https://ijnaa.semnan.ac.ir/article_2351_0cc225d42285c772edd3782614976e89.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2017
8
1
The operators over the GIFS
Ezzatallah
Baloui Jamkhaneh
In 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.
Generalized intuitionistic fuzzy sets
intuitionistic fuzzy sets
modal-like operators
level operators
2017
04
01
11
21
https://ijnaa.semnan.ac.ir/article_2402_aa76bd23f45666bcc4956b21e9d4975a.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2017
8
1
On genuine Lupac{s}-Beta operators and modulus of continuity
Vijay
Gupta
Th.M.
Rassias
Ekta
Pandey
In 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.
factorial polynomials
Beta basis function
direct estimates
weighted modulus of continuity
$K$-functionals
2017
04
30
23
32
https://ijnaa.semnan.ac.ir/article_2307_251220725692ce599b98103f8f8d9cb7.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2017
8
1
Stability for certain subclasses of harmonic univalent functions
Ali
Ebadian
Saman
Azizi
Shahram
Najafzadeh
In 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.
Stability of the convolution
Integral convolution
Harmonic univalent
starlike and convex functions
2017
05
05
33
45
https://ijnaa.semnan.ac.ir/article_2405_54526c108d6aa80a97f3ae45556c5eb9.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2017
8
1
Hermite-Hadamard inequality for geometrically quasiconvex functions on co-ordinates
Ali
Barani
Fatemeh
Malmir
In 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.
Hermite-Hadamard inequality
convex functions on co-ordinates
geometrically quasiconvex functions
2017
04
01
47
60
https://ijnaa.semnan.ac.ir/article_483_550a263fc24bc744472c0dbaf671d46c.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2017
8
1
Study on efficiency of the Adomian decomposition method for stochastic differential equations
Kazem
Nouri
Many 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.
Stochastic differential equation
stochastic Adomian decomposition method
Ito formula
2017
04
01
61
68
https://ijnaa.semnan.ac.ir/article_484_4f610d5f55a6031e073c4611c3719299.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2017
8
1
A spline collocation method for integrating a class of chemical reactor equations
Abdelmajid
Elhajaji
Nadia
Barje
Abdelhafid
Serghini
Khalid
Hilal
El Bekkaye
Mermri
. 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.
Partial differential equations
Distributed parameter systems
Plus flow reactors
Perturbed systems
Spline collocation method
2017
06
05
69
80
https://ijnaa.semnan.ac.ir/article_2495_adb58540af82056f951db7c7fef91870.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2017
8
1
Uncertainty in linear fractional transportation problem
Mohammad Reza
Safi
Seyyed Mojtaba
Ghasemi
In 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.
Transportation Problem
Linear Fractional Programming
Un- certain Measure
Uncertain Variable
Uncertain Programming
2017
04
10
81
93
https://ijnaa.semnan.ac.ir/article_504_5a23516c8827427da952623d3f103bcb.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2017
8
1
Dhage iteration method for PBVPs of nonlinear first order hybrid integro-differential equations
Bapurao
Dhage
In 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.
Hybrid differential equation
Hybrid fixed point theorem
Dhage iteration method
Existence and approximation theorems
2017
06
05
95
112
https://ijnaa.semnan.ac.ir/article_2349_b7c0d94e0bbcfba713b9b9348f61bcb3.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2017
8
1
The James and von Neumann-Jordan type constants and uniform normal structure in Banach spaces
Mina
Dinarvand
Recently, 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.
James type constant
von Neumann-Jordan type constant
Ptolemy constant
Fixed point property
Uniform normal structure
2017
06
05
113
122
https://ijnaa.semnan.ac.ir/article_2348_fc7c782f405f0e55f30d9c0a19a1e90d.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2017
8
1
Convergence of trajectories in infinite horizon optimization
Sara
Hassani
Musa
Mammadov
In 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.
Infinite horizon optimization
Ideal convergence
statistical convergence
2017
06
06
123
131
https://ijnaa.semnan.ac.ir/article_2496_45dd23662834206d7ecfd588dc09e613.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2017
8
1
Some results on coupled fixed point and fixed point theory in partially ordered probabilistic like (quasi) Menger spaces
Hamid
Shayanpour
Asiyeh
Nematizadeh
In 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).
Coupled fixed point
Partially ordered PLM-space (PLqM-space)
Mixed monotone property
2017
04
01
133
157
https://ijnaa.semnan.ac.ir/article_2350_7593b3a47ec39cd8354660d43a2a3a78.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2017
8
1
On the metric triangle inequality
Alexandre
Mihai Bica
A 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.
Generalized metric space
Triangle inequality
Separated topologies
non-Euclidean geometry
2017
04
01
159
164
https://ijnaa.semnan.ac.ir/article_2497_ec86ad0629d277b3dfc9ff8de6b43e4b.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2017
8
1
Existence results for equilibrium problems under strong sign property
Somaye
Jafari
Ali
Farajzadeh
This 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.
metric linear space
equilibrium problem
Minty equilibrium problem
strong upper sign property
2017
04
01
165
176
https://ijnaa.semnan.ac.ir/article_2498_1ac673c544179be70aa77273e99be930.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2017
8
1
Unsteady free convection oscillatory couette flow through a variable porous medium with concentration profile
Surjan
Singh
Pawan
Kumar Sharma
Kavindra
Nath Rai
Nagendra
Singh Tomer
In 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.
Coutte flow
variable porous medium
concentration profile
oscillatory plates
2017
06
06
177
186
https://ijnaa.semnan.ac.ir/article_2499_b3cd9cde6f5d728052f0bfa1991e4bcf.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2017
8
1
Almost n-Multiplicative Maps between Frechet Algebras
Taher
Ghasemi Honary
Mashaalah
Omidi
AmirHossein
Sanatpour
For 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 $ngeq 2$.
multiplicative maps (homomorphisms)
Almost multiplicative maps
automatic continuity
Frechet algebras
Banach algebras
2017
06
06
187
195
https://ijnaa.semnan.ac.ir/article_2500_05334ad00015c7183c16bcaeeaa21ae5.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2017
8
1
On the real quadratic fields with certain continued fraction expansions and fundamental units
Ozen
Ozer
Ahmed
Khammash
The 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.
Quadratic Field
Fundamental Unit
Continued Fraction Expansion
Class Number
2017
06
24
197
208
https://ijnaa.semnan.ac.ir/article_2570_f031084ca84601432b4d0a9b9ec8e67d.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2017
8
1
$C$-class and $F(psi,varphi)$-contractions on $M$-metric spaces
Hossein
Monfared
Mahdi
Azhini
Mehdi
Asadi
Partial 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.
Fixed point
Partial metric space
$M$-metric space
2017
06
06
209
224
https://ijnaa.semnan.ac.ir/article_2502_9859ace6f794b72f4e7dcfdcef8fbe62.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2017
8
1
Hermite-Hadamard inequalities for $mathbb{B}$-convex and $mathbb{B}^{-1}$-convex functions
Ilknur
Yesilce
Gabil
Adilov
Hermite-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.
Hermite-Hadamard inequality
$mathbb{B}$-convex functions
$mathbb{B}^{-1}$-convex functions
abstract convexity
2017
04
01
225
233
https://ijnaa.semnan.ac.ir/article_2503_47aad633f8dde9d4ebbec7a4f5100c63.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2017
8
1
Some properties of analytic functions related with bounded positive real part
Rahim
Kargar
Ali
Ebadian
Janusz
Sokol
In this paper, we define new subclass of analytic functions related with bounded positive real part, and coefficients estimates, duality and neighborhood are considered.
starlike function
duality
Hadamard product
subordination
neighborhood
2017
06
07
235
244
https://ijnaa.semnan.ac.ir/article_2397_5dc76a49635a49e0934c56bd1d62a67c.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2017
8
1
Strong and $Delta$-convergence theorems for total asymptotically nonexpansive mappings in CAT(0)
G.S.
Saluja
Hemant Kumar
Nashine
Yumnam Rohen
Singh
In 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.
total asymptotically nonexpansive mapping
$Delta$-convergence
strong convergence
Noor iteration process
CAT(0) space
2017
06
08
245
260
https://ijnaa.semnan.ac.ir/article_2504_4f42776057d80c7ee758a87c0e9d7781.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2017
8
1
A note on the Young type inequalities
Leila
Nasiri
Mahmood
Shakoori
Wenshi
Liao
In 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].
Young inequality
Hilbert-Schmidt norm
Positive semidefinite matrices
Refinements
2017
06
11
261
267
https://ijnaa.semnan.ac.ir/article_2506_a808c7d7d539b34d6ab843f781924432.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2017
8
1
An inexact alternating direction method with SQP regularization for the structured variational inequalities
Abdellah
Bnouhachem
Th.M.
Rassias
In 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.
Variational inequalities
monotone operator
square quadratic proximal method
logarithmic-quadratic proximal method
alternating direction method
2017
04
01
269
289
https://ijnaa.semnan.ac.ir/article_2509_9008cf901d3dc9e7ee50dae1dfcd52d0.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2017
8
1
Similarity measurement for describe user images in social media
Alireza
Tavakoli Targhi
Online 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.
Similarity Measurement Web mining
Health Topics
Computer vision
Machine Learning Models
2017
06
12
291
299
International Journal of Nonlinear Analysis and Applications
IJNAA
2017
8
1
Periodic boundary value problems for controlled nonlinear impulsive evolution equations on Banach spaces
Said
Melliani
Lalla Saadia
Chadli
Abdelati
El Allaoui
This 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.
impulsive evolution equations
Periodic boundary value problems
Control
Mild solutions
2017
06
12
301
314
https://ijnaa.semnan.ac.ir/article_2511_9c928d75339bfb53c6c6d7d33589f99b.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2017
8
1
Fixed and coincidence points for hybrid rational Geraghty contractive mappings in ordered $b$-metric spaces
Arsalan
Ansari
Abdolrahman
Razani
Nawab
Hussain
In 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.
Fixed point
Coincidence point
ordered $b$-metric space
2017
06
12
315
329
https://ijnaa.semnan.ac.ir/article_453_1af16f96e2bd98fc07f75a2ba92620bb.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2017
8
1
New integral inequalities for $s$-preinvex functions
Badreddine
Meftah
In 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.
Integral inequality
$s$-preinvex function
H"{o}lder inequality
power mean inequality
2017
06
13
331
336
https://ijnaa.semnan.ac.ir/article_2513_0bf0cb71a40e7530f29390a2af97814d.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2017
8
1
Some extensions of Darbo's theorem and solutions of integral equations of Hammerstein type
Reza
Allahyari
Asadollah
Aghajani
In 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.
Measure of noncompactness
Quadratic integral equation
Darbo fixed point theorem
2017
06
13
337
351
https://ijnaa.semnan.ac.ir/article_2516_53794ed15760aa0136631bfa489ca584.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2017
8
1
On new faster fixed point iterative schemes for contraction operators and comparison of their rate of convergence in convex metric spaces
Cristian
Alecsa
In 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.
convex metric space
Fixed point
iterative algorithm
rate of convergence
convex combination
2017
06
13
353
388
https://ijnaa.semnan.ac.ir/article_2523_4466d793e9cc175859682633bda03bb0.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2017
8
1
The structure of ideals, point derivations, amenability and weak amenability of extended Lipschitz algebras
Maliheh
Mayghani
Davood
Alimohammadi
Let $(X,d)$ 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.
Amenability
Banach function algebra
extended Lipschitz algebra
point derivation
weak amenability
2017
04
01
389
404
https://ijnaa.semnan.ac.ir/article_493_c33ba9a36bbd03e49c6d1e1671e3f46e.pdf