Stability of an additive-quartic functional equation in modular spaces

Abstract

In this paper, we prove the Ulam-Hyers stability of the following additive-quartic functional equationin modular spaces by using the direct method.

Approximation of almost quadratic mappings via modular functional

“…Concerning stability problems of functional equations in modular spaces, Sadeghi [19] has proved generalized Hyers-Ulam stability via the fixed point method of a generalized Jensen functional equation f(rx + sy) = rg(x) + sh(y) in convex modular spaces with the Fatou property satisfying ∆ 2 -condition with 0 < κ 2. Recently, many mathematicians have established stability theorems of various functional equations in modular spaces (see, e.g., [8,12,[14][15][16]).…”

Stability of a Quadratic-Reciprocal Functional Equation: Direct Method

“…In 2008, a special case of Gavruta's theorem for the unbounded Cauchy difference was obtained by Ravi et al [22] by considering the summation of both the sum and the product of two p-norms in the sprite of Rassias approach and is named J. M. Rassias Stability of functional equation. Last seven decades the stability problems of several functional equations have been extensively investigated by a number of authors and there are many interesting results concerning this problem (see Gavruta [7], Karthikeyan et al [9][10][11], Rassias et al [20], and Ravi et al [22]).…”

Stability Results of Additive-Quadratic \(n\)-Dimensional Functional Equation

“…In 2008, a special case of Gavruta's theorem for the unbounded Cauchy difference was obtained by Ravi et al [27] by considering the summation of both the sum and the product of two p-norms in the spirit of Rassias approach. The stability problems of several functional equations have been extensively investigated by a number of authors and there are many interesting results concerning this problem (see [2,4,5,17,18,22,27]) and reference cited there in.…”