On the stability of an affine functional equation

Abstract

In this paper, we obtain the general solution and we prove the generalized Hyers-Ulam stability for an affine functional equation.

ADDITIVE Ρ-Functional INEQUALITIES IN Β-Homogeneous F-Spaces

“…Cholewa [5] noticed that the theorem of Skof is still true if the relevant domain 320 Harin Lee, Jae Young Cha, Min Woo Cho & Myungjun Kwon E 1 is replaced by an Abelian group. The stability problems of various functional equations have been extensively investigated by a number of authors (see [1,3,4,6,9,10,11,12,13,15,17,18,19,20,21,24,25]). Definition 1.1.…”

Approximation of an Additive ϱ1,ϱ2-Random Operator Inequality

“…In [16,17], the authors studied the stability problem for fractional equations. Next, Cȃdariu et al [18][19][20] applied the fixed point method to solve the stability problem, and their work was continued by Keltouma et al [21], Park et al [22,23], Jung and Lee [24], and Brzdȩk and Ciepliński [25], see also [26,27].…”

STABILITY OF AN ADDITIVE (ρ1, ρ2)-FUNCTIONAL INEQUALITY IN BANACH SPACES

“…Park [18,19] defined additive ρ-functional inequalities and proved the HyersUlam stability of the additive ρ-functional inequalities in Banach spaces and nonArchimedean Banach spaces. The stability problems of various functional equations have been extensively investigated by a number of authors (see [1,3,7,10,17,20,21,24,25,26,27,30,31]). …”