Hyers\u2013Ulam stability of functional inequalities: a fixed point approach

Afshan Batool,Ozgur Ege,Manuel De La Sen,Sundas Nawaz

doi:10.1186/s13660-020-02520-8

Abstract

Using the fixed point method, we prove the Hyers–Ulam stability of a cubic and quartic functional equation and of an additive and quartic functional equation in matrix Banach algebras.

Highlights

Introduction and preliminariesUlam [30] raised a question concerning the stability of group homomorphisms
This paper is organized as follows: In Sects. 2 and 3, using the fixed point method, we prove the Hyers–Ulam stability of the cubic and quartic functional equation f (2x + y) + f (2x – y) = 3f (x + y) + f (–x – y) + 3f (x – y) + f (y – x)
Using the fixed point method, we prove the Hyers–Ulam stability of the functional equation Df (x, y) = 0 in matrix Banach algebras: an even case

Summary

Introduction

Introduction and preliminariesUlam [30] raised a question concerning the stability of group homomorphisms. By a similar method to the proof of Theorem 3.1, one can show that there exists a unique cubic mapping C : X → Y satisfying fn [xij] – fn –[xij] – Qn [xij]

Results

Conclusion