2020-01-24T05:27:35Z
https://ijnaa.semnan.ac.ir/?_action=export&rf=summon&issue=366
International Journal of Nonlinear Analysis and Applications
IJNAA
2017
8
2
Existence of common best proximity points of generalized $S$-proximal contractions
Hemant
Nashine
Zoran
Kadelburg
In this article, we introduce a new notion of proximal contraction, named as generalized S-proximal contraction and derive a common best proximity point theorem for proximally commuting non-self mappings, thereby yielding the common optimal approximate solution of some fixed point equations when there is no common solution. We furnish illustrative examples to highlight our results. We extend some results existing in the literature.
common best proximity point
optimal approximate solution
proximally commuting mappings
2017
12
01
1
8
https://ijnaa.semnan.ac.ir/article_2764_4a0f5785686f6c06e1cccf3bf040f1c4.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2017
8
2
On the natural stabilization of convection diffusion problems using LPIM meshless method
Ali
Arefmanesh
Mahmoud
Abbaszadeh
By using the finite element $p$-Version in convection-diffusion problems, we can attain to a stabilized and accurate results. Furthermore, the fundamental of the finite element $p$-Version is augmentation degrees of freedom. Based on the fact that the finite element and the meshless methods have similar concept, it is obvious that many ideas in the finite element can be easily used in the meshless methods. Hence, in this study, the concept of the finite element $p$-Version is applied in the LPIM meshfree method. The results prove that increasing degrees of freedom limits artificial numerical oscillations occurred in very large Peclet numbers.
convection-diffusion problems
LPIM meshless method
natural stabilization
$p$-Version finite element method
2017
12
07
9
22
https://ijnaa.semnan.ac.ir/article_466_bbb3a1fc16ee7db611610410e3835c9f.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2017
8
2
Contractive gauge functions in strongly orthogonal metric spaces
Maryam
Ramezani
Hamid
Baghani
Existence of fixed point in orthogonal metric spaces has been initiated recently by Eshaghi and et al. [On orthogonal sets and Banach fixed Point theorem, Fixed Point Theory, in press]. In this paper, we introduce the notion of the strongly orthogonal sets and prove a genuine generalization of Banach' fixed point theorem and Walter's theorem. Also, we give an example showing that our main theorem is a real generalization of these fixed point theorems.
strongly orthogonal set
Fixed point
gauge function
2017
12
03
23
28
https://ijnaa.semnan.ac.ir/article_452_2a1a25491ed3b19576dc43dcff80d39b.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2017
8
2
Perfect $2$-colorings of the Platonic graphs
Mohammad Hadi
Alaeiyan
Hamed
Karami
In this paper, we enumerate the parameter matrices of all perfect $2$-colorings of the Platonic graphs consisting of the tetrahedral graph, the cubical graph, the octahedral graph, the dodecahedral graph, and the icosahedral graph.
Perfect Coloring
Equitable Partition
Platonic Graph
2017
12
04
29
35
https://ijnaa.semnan.ac.ir/article_455_b232654319dc2a0cb031bc04091ece3d.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2017
8
2
Nonstandard explicit third-order Runge-Kutta method with positivity property
Mohammad
Mehdizadeh Khalsaraei
When one solves differential equations, modeling physical phenomena, it is of great importance to take physical constraints into account. More precisely, numerical schemes have to be designed such that discrete solutions satisfy the same constraints as exact solutions. Based on general theory for positivity, with an explicit third-order Runge-Kutta method (we will refer to it as RK3 method) positivity is not ensured when applied to the inhomogeneous linear systems and the same result is regained on nonlinear positivity for this method. Here we mean by positivity that the nonnegativity of the components of the initial vector is preserved. Nonstandard finite differences (NSFDs) schemes can improve the accuracy and reduce computational costs of traditional finite difference schemes. In addition to NSFDs produce numerical solutions which also exhibit essential properties of solution. In this paper, we investigate the positivity property for nonstandard RK3 method when applied to the numerical solution of special nonlinear initial value problems (IVPs) for ordinary differential equations (ODEs). We obtain new results for positivity which are important in practical applications. We provide some numerical examples to illustrate our results.
Positivity
Initial value problems
Advection equation
Bergers' equation
Runge-Kutta methods
2017
12
01
37
46
https://ijnaa.semnan.ac.ir/article_480_bfe54710147d214731391df012a6a25a.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2017
8
2
Curvature collineations on Lie algebroid structure
Esa
Sharahi
Esmaeil
Peyghan
Constantin
Arcus
Considering prolongation of a Lie algebroid equipped with a spray, defining some classical tensors, we show that a Lie symmetry of a spray is a curvature collineation for these tensors.
Curvature collineation
Lie algebroid
Lie symmetry
projectable section
spray
2017
12
01
47
63
https://ijnaa.semnan.ac.ir/article_516_59906f46ca9f8631db7aac16657b95ac.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2017
8
2
On the stability of linear differential equations of second order
Abbas
Najati
Mohammad
Abdollahpour
Choonkil
Park
The aim of this paper is to investigate the Hyers-Ulam stability of the linear differential equation<br />$$y''(x)+alpha y'(x)+beta y(x)=f(x)$$<br />in general case, where $yin C^2[a,b],$ $fin C[a,b]$ and $-infty<a<b<+infty$. The result of this paper improves a result of Li and Shen [textit{Hyers-Ulam stability of linear differential equations of second order,} Appl. Math. Lett. 23 (2010) 306--309].
Hyers-Ulam stability
linear differential equation of second order
2017
12
06
65
70
https://ijnaa.semnan.ac.ir/article_2768_c56749cc1ab49441e4b381aa39b132e9.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2017
8
2
Soft double fuzzy semi-topogenous structures
A.
Ghareeb
O.H.
Khalil
The purpose of this paper is to introduce the concept of soft double fuzzy semi-topogenous order. Firstly, we give the definition of soft double fuzzy semi-topogenous order. Secondly, we induce a soft double fuzzy topology from a given soft double fuzzy semi-topogenous order by using soft double fuzzy interior operator.
soft double fuzzy topology
soft double fuzzy interior operator
soft double fuzzy semi-topogenous structure
2017
12
01
71
88
https://ijnaa.semnan.ac.ir/article_2788_42478fba2bdf9494bd980f7308e1f221.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2017
8
2
Interpolation of fuzzy data by using flat end fuzzy splines
Reza
Ezzati
Saeid
Abbasbandy
Hossein
Behforooz
In this paper, a new set of spline functions called ``Flat End Fuzzy Spline" is defined to interpolate given fuzzy data. Some important theorems on these splines together with their existence and uniqueness properties are discussed. Then numerical examples are presented to illustrate the differences between of using our spline and other interpolations that have been studied before.
fuzzy interpolation
extension principle
fuzzy splines
2017
12
01
89
97
https://ijnaa.semnan.ac.ir/article_2765_d76b656bd725808a80f0451c76bd26b8.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2017
8
2
Translation invariant mappings on KPC-hypergroups
Seyyed Mohammad
Tabatabaie
Faranak
Haghighifar
In this paper, we give an extension of the Wendel's theorem on KPC-hypergroups. We also show that every translation invariant mapping is corresponding with a unique positive measure on the KPC-hypergroup.
DJS-hypergroup
KPC-hypergroup
Translation Invariant Mapping
Wendel's Theorem
2017
12
01
99
107
https://ijnaa.semnan.ac.ir/article_2785_050eaa7a4eae270a339a107852a64608.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2017
8
2
Some new Ostrowski type fractional integral inequalities for generalized $(r;g,s,m,varphi)$-preinvex functions via Caputo $k$-fractional derivatives
Artion
Kashuri
Rozana
Liko
In the present paper, the notion of generalized $(r;g,s,m,varphi)$-preinvex function is applied to establish some new generalizations of Ostrowski type integral inequalities via Caputo $k$-fractional derivatives. At the end, some applications to special means are given.
Ostrowski type inequality
H"{o}lder's inequality
Minkowski's inequality
$s$-convex function in the second sense
$m$-invex
2017
12
01
109
124
https://ijnaa.semnan.ac.ir/article_2790_0b41c4fb5b26b287e9fc35c76b4ec926.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2017
8
2
Mathematical modeling of optimized SIRS epidemic model and some dynamical behavior of the solution
Mehdi
Nadjafikhah
Saeid
Shagholi
In this paper, a generalized mathematical model of spread of infectious disease as SIRS epidemic model is considered as a nonlinear system of differential equation. We prove that for positive initial conditions the resulting equivalence system has positive solution and under some hypothesis, this system with initial positive condition, has a positive $T$-periodic solution which is globally asymptotically stable. For numerical simulations the fourth order Runge-Kutta method is applied to the nonlinear system of differential equations.
Mathematical modeling
epidemic SIRS model
positive solution
globally asymptotically stability
2017
12
01
125
134
https://ijnaa.semnan.ac.ir/article_2792_035182d58bb9842edde0597201b211da.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2017
8
2
Modified degenerate Carlitz's $q$-bernoulli polynomials and numbers with weight ($alpha ,beta $)
Ugur
Duran
Mehmet
Acikgoz
The main goal of the present paper is to construct some families of the Carlitz's $q$-Bernoulli polynomials and numbers. We firstly introduce the modified Carlitz's $q$-Bernoulli polynomials and numbers with weight ($_{p}$. We then define the modified degenerate Carlitz's $q$-Bernoulli polynomials and numbers with weight ($alpha ,beta $) and obtain some recurrence relations and other identities. Moreover, we derive some correlations with the modified Carlitz's $q$-Bernoulli polynomials with weight ($alpha ,beta $), the modified degenerate Carlitz's $q$-Bernoulli polynomials with weight ($alpha ,beta $), the Stirling numbers of the first kind and second kind.
Carlitz's $q$-Bernoulli polynomials
Stirling numbers of the first kind
Stirling numbers of the second kind
$p$-adic $q$-integral
2017
12
01
135
144
https://ijnaa.semnan.ac.ir/article_2791_48a0eba5d8560ea93b810f1b3562b4eb.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2017
8
2
Coupled coincidence point and common coupled fixed point theorems in complex valued metric spaces
Fayyaz
Rouzkard
Mohammad
Imdad
In this paper, we introduce the concept of a w-compatible mappings and utilize the same to discuss the ideas of coupled coincidence point and coupled point of coincidence for nonlinear contractive mappings in the context of complex valued metric spaces besides proving existence theorems which are following by corresponding unique coupled common fixed point theorems for such mappings. Some illustrative examples are also given to substantiate our newly proved results.
Common fixed point
Contractive type mapping
coupled coincidence point
coupled point of coincidence
Complex valued metric space
2017
12
01
145
158
https://ijnaa.semnan.ac.ir/article_521_2a61f222299a2c5adf3e26b8819aaa3a.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2017
8
2
Global attractor for a nonlocal hyperbolic problem on ${mathcal{R}}^{N}$
Perikles
Papadopoulos
N.L.
Matiadou
We consider the quasilinear Kirchhoff's problem<br />$$ u_{tt}-phi (x)||nabla u(t)||^{2}Delta u+f(u)=0 ,;; x in {mathcal{R}}^{N}, ;; t geq 0,$$<br />with the initial conditions $ u(x,0) = u_0 (x)$ and $u_t(x,0) = u_1 (x)$, in the case where $N geq 3, ; f(u)=|u|^{a}u$ and $(phi (x))^{-1} in L^{N/2}({mathcal{R}}^{N})cap L^{infty}({mathcal{R}}^{N} )$ is a positive function. The purpose of our work is to study the long time behaviour of the solution of this equation. Here, we prove the existence of a global attractor for this equation in the strong topology of the space ${cal X}_{1}=:{cal D}^{1,2}({mathcal{R}}^{N}) times L^{2}_{g}({mathcal{R}}^{N}).$ We succeed to extend some of our earlier results concerning the asymptotic behaviour of the solution of the problem.
quasilinear hyperbolic equations
Kirchhoff strings
global attractor
generalised Sobolev spaces
weighted $L^p$ Spaces
2017
12
01
159
168
https://ijnaa.semnan.ac.ir/article_2793_ef30a57e5aaa4eb687c61b37a80ea4d1.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2017
8
2
Computational method based on triangular operational matrices for solving nonlinear stochastic differential equations
Mahnaz
Asgari
Morteza
khodabin
In this article, a new numerical method based on triangular functions for solving nonlinear stochastic differential equations is presented. For this, the stochastic operational matrix of triangular functions for It^{o} integral are determined. Computation of presented method is very simple and attractive. In addition, convergence analysis and numerical examples that illustrate accuracy and efficiency of the method are presented.
Brownian motion
It^{o} integral
Nonlinear stochastic differential equation
Stochastic operational matrix
Triangular function
2017
12
01
169
179
https://ijnaa.semnan.ac.ir/article_2783_c6fbfe31fd6236b020f1a1ec4c88ae52.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2017
8
2
On the approximation by Chlodowsky type generalization of (p,q)-Bernstein operators
Khursheed
Ansari
Ali
Karaisa
In the present article, we introduce Chlodowsky variant of $(p,q)$-Bernstein operators and compute the moments for these operators which are used in proving our main results. Further, we study some approximation properties of these new operators, which include the rate of convergence using usual modulus of continuity and also the rate of convergence when the function $f$ belongs to the class Lip$_{M}(alpha )$. Moreover, we also discuss convergence and rate of approximation in weighted spaces and weighted statistical approximation properties of the sequence of positive linear operators defined by us.
$(p,q)$-integers
Bernstein operators
positive linear operators
Korovkin type approximation theorem
statistical approximation
2017
12
01
181
200
https://ijnaa.semnan.ac.ir/article_2789_8c00a08033e702b77e6d822b3272f202.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2017
8
2
A necessary condition for multiple objective fractional programming
Rezvan
Kamali
Ali
Davari
In this paper, we establish a proof for a necessary condition for multiple objective fractional programming. In order to derive the set of necessary conditions, we employ an equivalent parametric problem. Also, we present the related semi parametric model.
Multiple objective fractional programming
Generalized n-set convex function
Efficient solution
2017
12
01
201
207
https://ijnaa.semnan.ac.ir/article_482_73a53fecfb7bfc8a6778a60cabed4272.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2017
8
2
On generalized Hermite-Hadamard inequality for generalized convex function
Mehmet Zeki
Sarikaya
Huseyin
Budak
In this paper, a new inequality for generalized convex functions which is related to the left side of generalized Hermite-Hadamard type inequality is obtained. Some applications for some generalized special means are also given.
Generalized Hermite-Hadamard inequality
Generalized H"{o}lder inequality
Generalized convex functions
2017
12
01
209
222
https://ijnaa.semnan.ac.ir/article_2797_fe30c34bcf477187700e2c4e5c003604.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2017
8
2
Analytical aspects of the interval unilateral quadratic matrix equations and their united solution sets
Tayyebe
Haqiri
Azim
Rivaz
Mahmoud
Mohseni Moghadam
This paper introduces the emph{interval unilateral quadratic matrix equation}, $IUQe$ and attempts to find various analytical results on its AE-solution sets in which $A,B$ and $CCC$ are known real interval matrices, while $X$ is an unknown matrix. These results are derived from a generalization of some results of Shary. We also give sufficient conditions for non-emptiness of some quasi-solution sets, provided that $A$ is regular. As the most common case, the united solution set has been studied and two direct methods for computing an outer estimation and an inner estimation of the united solution set of an interval unilateral quadratic matrix equation are proposed. The suggested techniques are based on nonlinear programming as well as sensitivity analysis.
AE-solution sets
interval unilateral quadratic matrix equation
united solution set
nonlinear programming
Sensitivity analysis
2017
12
20
223
241
https://ijnaa.semnan.ac.ir/article_2796_50bf006dbe46ff6c42b14348865a347c.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2017
8
2
On exponential domination and graph operations
Betul
Atay
Aysun
Aytac
An exponential dominating set of graph $G = (V,E )$ is a subset $Ssubseteq V(G)$ such that $sum_{uin S}(1/2)^{overline{d}{(u,v)-1}}geq 1$ for every vertex $v$ in $V(G)-S$, where $overline{d}(u,v)$ is the distance between vertices $u in S$ and $v in V(G)-S$ in the graph $G -(S-{u})$. The exponential domination number, $gamma_{e}(G)$, is the smallest cardinality of an exponential dominating set. Graph operations are important methods for constructing new graphs, and they play key roles in the design and analysis of networks. In this study, we consider the exponential domination number of graph operations including edge corona, neighborhood corona and power.
Graph vulnerability
network design and communication
exponential domination number
edge corona
neighbourhood corona
2017
12
01
243
250
https://ijnaa.semnan.ac.ir/article_2767_30d3be476f5e7e4708605bbc92f6406d.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2017
8
2
$(varphi_1, varphi_2)$-variational principle
Abdelhakim
Maaden
Stouti
Abdelkader
In this paper we prove that if $X $ is a Banach space, then for every lower semi-continuous bounded below function $f, $ there exists a $left(varphi_1, varphi_2right)$-convex function $g, $ with arbitrarily small norm, such that $f + g $ attains its strong minimum on $X. $ This result extends some of the well-known varitional principles as that of Ekeland [On the variational principle, J. Math. Anal. Appl. 47 (1974) 323--353], that of Borwein-Preiss [A smooth variational principle with applications to subdifferentiability and to differentiability of convex functions, Trans. Amer. Math. Soc. 303 (1987) 517--527] and that of Deville-Godefroy-Zizler [Un principe variationel utilisant des fonctions bosses, C. R. Acad. Sci. (Paris). Ser.I 312 (1991) 281--286] and [A smooth variational principle with applications to Hamilton-Jacobi equations in infinite dimensions, J. Funct. Anal. 111 (1993) 197--212].
$left(varphi_1, varphi_2right)$-convex function
$left(varphi_1, varphi_2right)$-variational principle
Ekeland's variational principle
smooth variational principle
2017
12
22
251
261
https://ijnaa.semnan.ac.ir/article_2766_da52f80c47f3aee56ce7052c87770f23.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2017
8
2
Existence and uniqueness of the solution for a general system of operator equations in $b-$metric spaces endowed with a graph
Cristian
Chifu
Gabriela
Petrusel
The purpose of this paper is to present some coupled fixed point results on a metric space endowed with two $b$-metrics. We shall apply a fixed point theorem for an appropriate operator on the Cartesian product of the given spaces endowed with directed graphs. Data dependence, well-posedness and Ulam-Hyers stability are also studied. The results obtained here will be applied to prove the existence and uniqueness of the solution for a system of integral equations.
Fixed point
Coupled fixed point
$b$-metric space
connected graph
integral equations
2017
12
23
263
276
https://ijnaa.semnan.ac.ir/article_2800_62e25ec2b3418aa3f744b6478d9fbcde.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2017
8
2
Application of fractional-order Bernoulli functions for solving fractional Riccati differential equation
Yadollah
Ordokhani
Parisa
Rahimkhani
Esmail
Babolian
In this paper, a new numerical method for solving the fractional Riccati differential equation is presented. The fractional derivatives are described in the Caputo sense. The method is based upon fractional-order Bernoulli functions approximations. First, the fractional-order Bernoulli functions and their properties are presented. Then, an operational matrix of fractional order integration is derived and is utilized to reduce the under study problem to a system of algebraic equations. Error analysis included the residual error estimation and the upper bound of the absolute errors are introduced for this method. The technique and the error analysis are applied to some problems to demonstrate the validity and applicability of our method.
Fractional Riccati differential equation
Fractional-order Bernoulli functions
Caputo derivative
Operational matrix
Collocation method
2017
12
01
277
292
https://ijnaa.semnan.ac.ir/article_2795_3990006fa9915eb0af3345e8046f7bc8.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2017
8
2
On some fixed points properties and convergence theorems for a Banach operator in hyperbolic spaces
Akindele Adebayo
Mebawondu
Lateef
Jolaoso
Hammed
Abass
In this paper, we prove some fixed points properties and demiclosedness principle for a Banach operator in uniformly convex hyperbolic spaces. We further propose an iterative scheme for approximating a fixed point of a Banach operator and establish some strong and $Delta$-convergence theorems for such operator in the frame work of uniformly convex hyperbolic spaces. The results obtained in this paper extend and generalize corresponding results on uniformly convex Banach spaces, CAT(0) spaces and many other results in this direction.
Banach operator
uniformly convex hyperbolic spaces
strong and $Delta$-convergence theorem
Modified Picard Normal S-iteration
2017
12
01
293
306
https://ijnaa.semnan.ac.ir/article_2799_2ea33223c55fba3700f88bd7aefc3695.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2017
8
2
Some common fixed point theorems for four $(psi,varphi)$-weakly contractive mappings satisfying rational expressions in ordered partial metric spaces
Rashwan
Rashwan
S.M.
Saleh
The aim of this paper is to prove some common fixed point theorems for four mappings satisfying $(psi,varphi)$-weak contractions involving rational expressions in ordered partial metric spaces. Our results extend, generalize and improve some well-known results in the literature. Also, we give two examples to illustrate our results.
Common fixed point
rational contractions
ordered partial metric spaces
dominating and dominated mappings
2017
12
26
307
326
https://ijnaa.semnan.ac.ir/article_468_a5b9c5cc09ff9b3a978f98266a1b155a.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2017
8
2
Mazur-Ulam theorem in probabilistic normed groups
Alireza
Pourmoslemi
Kourosh
Nourouzi
In this paper, we give a probabilistic counterpart of Mazur-Ulam theorem in probabilistic normed groups. We show, under some conditions, that every surjective isometry between two probabilistic normed groups is a homomorphism.
Probabilistic normed groups
Invariant probabilistic metrics
Mazur-Ulam Theorem
2017
12
01
327
333
https://ijnaa.semnan.ac.ir/article_2786_313d118769848a5d41636e321e9950d6.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2017
8
2
Fixed point theorems for generalized quasi-contractions in cone $b$-metric spaces over Banach algebras without the assumption of normality with applications
Shaoyuan
Xu
Suyu
Cheng
Suzana
Aleksic
In this paper, we introduce the concept of generalized quasi-contractions in the setting of cone $b$-metric spaces over Banach algebras. By omitting the assumption of normality we establish common fixed point theorems for the generalized quasi-contractions with the spectral radius $r(lambda)$ of the quasi-contractive constant vector $lambda$ satisfying $r(lambda)in [0,frac{1}{s})$ in the setting of cone $b$-metric spaces over Banach algebras, where the coefficient $s$ satisfies $sge 1$. As consequences, we obtain common fixed point theorems for the generalized $g$-quasi-contractions in the setting of such spaces. The main results generalize, extend and unify several well-known comparable results in the literature. Moreover, we apply our main results to some nonlinear equations, which shows that these results are more general than corresponding ones in the setting of $b$-metric or metric spaces.
cone $b$-metric spaces over Banach algebras
non-normal cones
$c$-sequences
generalized quasi-contractions
Fixed point theorem
2017
12
01
335
353
https://ijnaa.semnan.ac.ir/article_2787_c82fdf395409faa23840674b2855da21.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2017
8
2
L$^q$ inequalities for the ${s^{th}}$ derivative of a polynomial
Ahmad
Zireh
Let $f(z)$ be an analytic function on the unit disk ${zinmathbb{C}, |z|leq 1}$, for each $q>0$, the $|f|_{q}$ is defined as follows<br />begin{align*}<br />begin{split}<br />&left|fright|_q:=left{frac{1}{2pi}int_0^{2pi}left|f(e^{itheta})right|^qdthetaright}^{1/q},<br /> 0<q<infty,\<br />&left|fright|_{infty}:=max_{|z|=1}left|f(z)right|.<br />end{split}<br />end{align*}<br /> Govil and Rahman [{it Functions of exponential type not vanishing in a half-plane and related polynomials}, { Trans. Amer. Math. Soc.} {137} (1969) 501--517] proved that if $p(z)$ is a polynomial of degree $n$, which does not vanish in $|z|<k$, where $kgeq 1$, then for each $q>0$,<br />begin{align*}<br />left|p'right|_{q}leq frac{n}{|k+z|_q}|p|_{q}.<br />end{align*}<br />In this paper, we shall present an interesting generalization and refinement of this result which include some previous results.
Derivative
Polynomial
$L^q$ Inequality
Maximum modulus
Restricted Zeros
2017
12
01
355
362
https://ijnaa.semnan.ac.ir/article_2801_1533fb6d1e1801bc30789ab8dc04255b.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2017
8
2
Dynamics of higher order rational difference equation $x_{n+1}=(alpha+beta x_{n})/(A + Bx_{n}+ Cx_{n-k})$
Abu Alhalawa
Muna
Mohammad
Saleh
The main goal of this paper is to investigate the periodic character, invariant intervals, oscillation and global stability and other new results of all positive solutions of the equation<br />$$x_{n+1}=frac{alpha+beta x_{n}}{A + Bx_{n}+ Cx_{n-k}},~~ n=0,1,2,ldots,$$<br />where the parameters $alpha$, $beta$, $A$, $B$ and $C$ are positive, and the initial conditions $x_{-k},x_{-k+1},ldots,x_{-1},x_{0}$ are positive real numbers and $kin{1,2,3,ldots}$. We give a detailed description of the semi-cycles of solutions and determine conditions under which the equilibrium points are globally asymptotically stable. In particular, our paper is a generalization of the rational difference equation that was investigated by Kulenovic et al. [The Dynamics of $x_{n+1}=frac{alpha +beta x_{n}}{A+Bx_{n}+ C x_{n-1}}$, Facts and Conjectures, Comput. Math. Appl. 45 (2003) 1087--1099].
stability theory
semi-cycle analysis
invariant intervals
nonlinear difference equations
discrete dynamical systems
2017
12
01
363
379
https://ijnaa.semnan.ac.ir/article_2794_5faa22d45bfb19c931f7a566b1d51774.pdf