
handle: 20.500.12128/15946
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 \(x,y\in S\).
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
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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