STABILITY OF JENSEN FUNCTIONAL EQUATIONS ON AMENABLE SEMIGROUPS

2019 ◽  
Vol 11 (1) ◽  
pp. 1-11
Author(s):  
Zahra Sarmast ◽  
Madjid Eshaghi ◽  
Nader Asghari ◽  
Amirhossein Rashmei
Keyword(s):  
Functional Equations ◽  
Jensen Functional ◽  
Amenable Semigroups

Stability of m-Jensen Functional Equations

2017 ◽  
Vol 24 (1) ◽  
pp. 1-12
Author(s):  
Teodoro Lara ◽  
Nelson Merentes ◽  
Roy Quintero ◽  
Edgar Rosales
Keyword(s):  
Functional Equations ◽  
Jensen Functional

scholarly journals On the stability of generalized d'Alembert and Jensen functional equations

2006 ◽  
Vol 2006 ◽  
pp. 1-12 ◽  
Author(s):  
Gwang Hui Kim ◽  
Sever S. Dragomir
Keyword(s):  
Stability Problem ◽  
Functional Equations ◽  
Jensen Functional ◽  
The Stability

The aim of this paper is to study the stability problem of the generalized d'Alembert, Wilson, and Jensen functional equations.

Non-Archimedean hyperstability of Cauchy–Jensen functional equations on a restricted domain

2018 ◽  
Vol 24 (2) ◽  
pp. 155-165
Author(s):  
Iz-iddine EL-Fassi
Keyword(s):  
Fixed Point ◽  
Functional Equations ◽  
Metric Spaces ◽  
Fixed Point Approach ◽  
Nonlinear Anal ◽  
Stability Of Functional Equations ◽  
Jensen Functional ◽  
Empty Subset ◽  
The Stability ◽  
Fixed Positive Integer

Abstract Let X be a normed space, {U\subset X\setminus\{0\}} a non-empty subset, and {(G,+)} a commutative group equipped with a complete ultrametric d that is invariant (i.e., {d(x+z,y+z)=d(x,y} ) for {x,y,z\in G} ). Under some weak natural assumptions on U and on the function {\gamma\colon U^{3}\to[0,\infty)} , we study the new generalized hyperstability results when {f\colon U\to G} satisfies the inequality d\biggl{(}\alpha f\biggl{(}\frac{x+y}{\alpha}+z\biggr{)},\alpha f(z)+f(y)+f(x)% \biggr{)}\leq\gamma(x,y,z) for all {x,y,z\in U} , where {\frac{x+y}{\alpha}+z\in U} and {\alpha\geq 2} is a fixed positive integer. The method is based on a quite recent fixed point theorem (Theorem 1 in [J. Brzdȩk and K. Ciepliński, A fixed point approach to the stability of functional equations in non-Archimedean metric spaces, Nonlinear Anal. 74 2011, 18, 6861–6867]) (cf. [8, Theorem 1]) in some functions spaces.

scholarly journals Asymptotic stability of the Cauchy and Jensen functional equations

2016 ◽  
Vol 150 (1) ◽  
pp. 131-141 ◽  
Author(s):  
A. Bahyrycz ◽  
Zs. Páles ◽  
M. Piszczek
Keyword(s):  
Asymptotic Stability ◽  
Functional Equations ◽  
Jensen Functional
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