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On the stability of the pexiderized trigonometric functional equation. (English) Zbl 1159.39013

Similar to his papers [Adv. Difference Equ. 2007, Article ID 90405 (2007; Zbl 1148.39024)] and [Banach J. Math. Anal. 1, No. 2, 227–236, electronic only (2007; Zbl 1129.39013)], the author investigates the superstability of the pexiderized trigonometric functional inequality

|f(x+y)+f(x-y)-2g(x)h(y)|ϕ(x)orϕ(y)

and also stability of the Jensen type functional inequality

|f(x+y)-f(x-y)-2f(y)|ψ(x,y)

for each x,yG, where (G,+) is an abelian group and the mappings f,g,h:G are unknown and ϕ:G and ψ:G×G are known. He also extends his results to the Banach algebras.


MSC:
39B82Stability, separation, extension, and related topics
39B52Functional equations for functions with more general domains and/or ranges
39B62Functional inequalities, including subadditivity, convexity, etc. (functional equations)