Generalized Hyers-Ulam Stability of Cubic Type Functional Equations in Normed Spaces

Abstract

In this paper, we solve the Hyers-Ulam stability problem for the following cubic type functional equationin quasi-Banach space and non-Archimedean space, where r = ±1, 0 and s are real numbers.

General solution and generalized Ulam - Hyers stability of ri􀀀 type n dimensional quadratic-cubic functional equation in random normed spaces: Direct and fixed point methods

“…K.W.Jun and H.M.Kim [15] considered the following functional equation f (2x+y)+ f (2x−y) = 2 f (x+y)+2 f (x−y)+12 f (x) (1.2) which is called a cubic functional equation and every solution of the cubic functional equation is said to be a cubic mapping. G.H.Kim, H.Y.Shin [20] introduced and investigated the generalized Ulam-Hyers Stability of the following more generalized cubic functional equation f (rx + sy) + f (rx − sy) = rs 2 f (x + y) + rs 2 f (x − y)…”