ON A FUNCTIONAL EQUATION ORIGINATING FROM A MIXED ADDITIVE AND CUBIC EQUATION AND ITS STABILITY

Abstract

In this paper, we study solutions of the 2-variable mixed additive andcubic functional equationf (2x + y, 2z + t) + f (2x − y, 2z − t) = 2f (x + y, z + t)+ 2f (x − y, z − t) + 2f (2x, 2z) − 4f (x, z),which has the cubic form f (x, y) = ax+ bx y + cxy+ dy as a solution. Also the Hyers–Ulam–Rassias stability of this equation in thenon-Archimedean Banach spaces is investigated.

Keywords

• Hyers–Ulam–Rassias stability, Cubic functional equation, Non–Archimedeannormed space, Derivation.

ON A FUNCTIONAL EQUATION ORIGINATING FROM A MIXED ADDITIVE AND CUBIC EQUATION AND ITS STABILITY

Abstract

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Keywords

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