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- W2962873770 abstract "In this paper. (1) We determine the complex-valued solutions of the following variant of Van Vleck's functional equation $$int_{S}f(sigma(y)xt)dmu(t)-int_{S}f(xyt)dmu(t) = 2f(x)f(y), ;x,yin S,$$ where $S$ is a semigroup, $sigma$ is an involutive morphism of $S$, and $mu$ is a complex measure that is linear combinations of Dirac measures $(delta_{z_{i}})_{iin I}$, such that for all $iin I$, $z_{i}$ is contained in the center of $S$. (2) We determine the complex-valued continuous solutions of the following variant of d'Alembert's functional equation $$int_{S}f(xty)dupsilon(t)+int_{S}f(sigma(y)tx)dupsilon(t) = 2f(x)f(y), ;x,yin S,$$ where $S$ is a topological semigroup, $sigma$ is a continuous involutive automorphism of $S$, and $upsilon$ is a complex measure with compact support and which is $sigma$-invariant. (3) We prove the superstability theorems of the first functional equation." @default.
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- W2962873770 date "2016-12-09" @default.
- W2962873770 modified "2023-09-27" @default.
- W2962873770 title "Solutions and stability of variant of Van Vleck's and D'Alembert's functional equations" @default.
- W2962873770 doi "https://doi.org/10.22075/ijnaa.2017.1803.1472" @default.
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