On stability and hyperstability of an equation characterizing multi-Cauchy-Jensen mappings
type: Item
instance of: scholarly article
title: On stability and hyperstability of an equation characterizing multi-Cauchy-Jensen mappings
zbMATH Open document ID: 1404.39026
author: Anna Bahyrycz
author: Jolanta Olko
published in: Results in Mathematics
publication date: 2018-07-23T00:00:00Z
review text: The concept of stability for a functional equation arises when one replaces a functional equation by inequality, which acts as a perturbation of the equation. In 1940 S. M. Ulam posed the first stability problem. In 1941 \textit{D. H. Hyers} [Proc. Natl. Acad. Sci. USA 27, 222--224 (1941; Zbl 0061.26403)] gave a partial affirmative answer to the question of Ulam. Hyers' Theorem was generalized by \textit{T. Aoki} [J. Math. Soc. Japan 2, 64--66 (1950; Zbl 0040.35501)] for additive mappings and by \textit{T. M. Rassias} [Proc. Am. Math. Soc. 72, 297--300 (1978; Zbl 0398.47040)] for linear mappings by considering an unbounded Cauchy difference. In the present work, the authors establish a new characterization of multi-Cauchy-Jensen mappings, which states that a function fulfilling some equation on a restricted domain is multi-Cauchy-Jensen on the whole space. Moreover, they proved that a function which approximately satisfies on restricted domain the equation characterizing such functions is close in some sense to the solution of the equation.
reviewed by: Ghadir Sadeghi
Mathematics Subject Classification ID: 39B52
Mathematics Subject Classification ID: 39B82
Mathematics Subject Classification ID: 39B72
Mathematics Subject Classification ID: 47H10
zbMATH DE Number: 6909674
zbMATH Keywords: Hyers-Ulam stability
zbMATH Keywords: multi-Cauchy-Jensen mapping
zbMATH Keywords: hyperstability
zbMATH Keywords: fixed point theorem
MaRDI profile type: Publication
full work available at URL: s00025-018-0815-8
OpenAlex ID: W2790443666
cites work: On the stability of the linear transformation in Banach spaces
cites work: ON THE SOLUTIONS OF A BI-JENSEN FUNCTIONAL EQUATION AND ITS STABILITY
cites work: SOLUTION OF A VECTOR VARIABLE BI-ADDITIVE FUNCTIONAL EQUATION
cites work: The Stability of Certain Functional Equations
cites work: Multi-affine and multi-Jensen functions and their connection with generalized polynomials
cites work: On a Cauchy-Jensen functional equation and its stability
cites work: On stability and hyperstability of an equation characterizing multi-additive mappings
cites work: On an equation characterizing multi-Cauchy-Jensen mappings and its Hyers-Ulam stability
cites work: Classes of transformations and bordering transformations
cites work: ON THE STABILITY OF A CAUCHY-JENSEN FUNCTIONAL EQUATION
cites work: Fixed point theory and the Ulam stability
cites work: A fixed point approach to stability of functional equations
cites work: Remarks on the Hyers-Ulam stability of some systems of functional equations
cites work: Recent developments of the conditional stability of the homomorphism equation
cites work: ON MULTI-JENSEN FUNCTIONS AND JENSEN DIFFERENCE
cites work: Stability of the multi-Jensen equation
cites work: Generalized stability of multi-additive mappings
cites work: Applications of fixed point theorems to the Hyers-Ulam stability of functional equations -- a survey
cites work: A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings
cites work: On the Stability of the Linear Functional Equation
cites work: Q3645888
cites work: On the generalized Hyers-Ulam stability of a Cauchy-Jensen functional equation
cites work: Hyers-Ulam-Rassias stability of functional equations in nonlinear analysis
cites work: Functional Equations and Inequalities with Applications
cites work: Q5439382
cites work: STABILITY OF THE MULTI-JENSEN EQUATION
cites work: On the Stability of the Linear Mapping in Banach Spaces
cites work: Some remarks on the stability of the multi-Jensen equation
Wikidata QID: Q130118863
DOI: 10.1007/S00025-018-0815-8
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description: scientific article; zbMATH DE number 6909674