Approximate mixed type additive and quartic functional equation

Abasalt Bodaghi

doi:10.5269/bspm.v35i1.29014

Abstract

In the current work, we introduce a general form of a mixed additive and quartic functional equation. We determine all solutions of this functional equation. We also establish the generalized Hyers-Ulam stability of this new functional equation in quasi-$\beta$-normed spaces.

Highlights

He proved the Hyers-Ulam Rassias stability of the functional equation (1.2) in real normed spaces
Bodaghi [4] presented a new form of the additivequartic functional equation which is different from (1.2) as follows: f
It is verified that the function f (x) = αx + βx4 is a solution of the functional equation (1.4)

Summary

Introduction

He proved the Hyers-Ulam Rassias stability of the functional equation (1.2) in real normed spaces. Other versions of a quartic functional equation can be found in [3], [17], [18] and [19]. In [14], Eshaghi Gordji introduced and obtained the general solution of the following mixed type additive and quartic functional equation f (2x + y) + f (2x − y) = 4{(f (x + y) + f (x − y)}

Objectives

Results

Conclusion