On a Quadratic-Trigonometric Functional Equation and Some Applications
نویسندگان
چکیده
منابع مشابه
Hyers-Ulam stability of a generalized trigonometric-quadratic functional equation
The Hyers-Ulam stability of the generalized trigonometric-quadratic functional equation ( ) ( ) ( ) ( ) ( ) ( ) 2 F x y G x y H x K y L x M y + − − = + + over the domain of an abelian group and the range of the complex field is established based on the assumption of the unboundedness of the function K. Subject to certain natural conditions, explicit shapes of the functions H and K are determine...
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In the present paper a solution of the generalizedquadratic functional equation$$f(kx+ y)+f(kx+sigma(y))=2k^{2}f(x)+2f(y),phantom{+} x,yin{E}$$ isgiven where $sigma$ is an involution of the normed space $E$ and$k$ is a fixed positive integer. Furthermore we investigate theHyers-Ulam-Rassias stability of the functional equation. TheHyers-Ulam stability on unbounded domains is also studied.Applic...
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A generalized trigonometric-quadratic functional equation of the form F(x+ y) + G(x− y) = 2H(x)K(y) + L(x) +M(y) over the domain of an abelian group and the range of the complex field is considered. Its stability is established based on the assumption that the function K is unbounded. Subject to certain natural conditions, explicit shapes of the functions H and K are determined. Several existin...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1995
ISSN: 0002-9947
DOI: 10.2307/2154805