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Stability of a generalized trigonometric functional equation

✍ Scribed by Janyarak Tongsomporn; Vichian Laohakosol; Charinthip Hengkrawit; Patanee Udomkavanich

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
308 KB
Volume
234
Category
Article
ISSN
0377-0427

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✦ Synopsis

The stability of the functional equation F (x + y) -G(xy) = 2H (x)K(y) over the domain of an abelian group G and the range of the complex field is investigated. Several related results extending a number of previously known ones, such as the ones dealing with the sine functional equation, the d'Alembert functional equation and Wilson functional equation, are derived as direct consequences. Applying the main result to the setting of Banach algebra, it is shown that if their operators satisfy a functional inequality and are subject to certain natural requirements, then these operators must be solutions of some well-known functional equations.

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