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Demonstratio Mathematica
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ON HYERS-ULAM STABILITY OF THE PEXIDER EQUATION

On Hyers-Ulam stability of the Pexider equation
Authors: Kominek, Zygfryd;

ON HYERS-ULAM STABILITY OF THE PEXIDER EQUATION

Abstract

The following result is proved. Theorem: Let \((S,+)\) be a commutative semigroup and let \(X\) be a~sequentially complete linear topological Hausdorff space. Assume that \(V\) is a sequentially closed, bounded, convex and symmetric with respect to zero subset of \(X\). For arbitrary functions \(f,g,h:S\to X\) satisfying the condition \[ f(x+y)-g(x)-h(y)\in V,\quad x,y\in S, \] there exist the functions \(f_1,g_1,h_1:S\to X\) such that \[ f_1(x+y)-g_1(x)-h_1(y)=0,\quad x,y\in S, \] \(f_1(x+y)-f(x+y)\in 15V\), \(g_1(x)-g(x)\in 7V\) and \(h_1(x)-h(x)\in 7V\) for all \(x,y\in S\).

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Keywords

linear topological Hausdorff space, functional equations, Pexider equation, Stability, separation, extension, and related topics for functional equations, Functional equations for functions with more general domains and/or ranges, Hyers-Ulam stability, Pexider functional equation, topological Hausdorff space

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
5
Average
Average
Average
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