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فهرست مقالات

Solutions and stability of variant of Van Vleck's and D'Alembert's functional equations

نویسنده:

علمی-پژوهشی (وزارت علوم)/ISC (23 صفحه - از 279 تا 301)

چکیده:

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.

کلیدواژه ها:

Homomorphism ،semigroup ،d'Alembert's equation ،Van Vleck's equation ،sine function ،involution ،multiplicative function ،superstability ،Van Vleck's equation, sine function ،multiplicative function, homomorphism, superstability


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