A Fixed Point Approach to Stability of Additive Functional Inequalities in Fuzzy Normed Spaces

Abstract

Abstract. In this paper, we investigate the solution of the following functional inequalityfor some fixed real number m with 1 3 < m ≤ 1 and using the fixed point method, we prove the generalized Hyers-Ulam stability for it in fuzzy Banach spaces.

Approximate Cubic Lie Derivations on ρ-Complete Convex Modular Algebras

“…In 2014, G. Sadeghi [16] has demonstrated generalized Hyers-Ulam stability via the fixed point method of a generalized Jensen functional equation ( + ) = ( ) + ℎ( ) in convex modular spaces with the Fatou property satisfying the Δ 2 -condition with 0 < ≤ 2. In [15], the authors have proved the generalized Hyers-Ulam stability of quadratic functional equations via the extensive studies of fixed point theory in the framework of modular spaces whose modulars are convex and lower semicontinuous but do not satisfy any relatives of Δ 2 -conditions (see also [17,18]). Recently, the authors [14,19,20] have investigated stability theorems of functional equations in modular spaces without using the Fatou property and Δ 2 -condition.…”