Fuzzy almost quadratic functions

TL;DR

This paper investigates the fuzzy stability of quadratic functional equations, establishing generalized stability results in fuzzy normed spaces for both the standard and Pexiderized quadratic equations.

Contribution

It introduces new fuzzy stability results for quadratic and Pexiderized quadratic equations, extending the classical stability framework to fuzzy normed spaces.

Findings

Fuzzy Hyers--Ulam--Rassias stability of quadratic equations established.

Generalized fuzzy stability results for Pexiderized quadratic equations proved.

Results extend stability phenomena to fuzzy normed space settings.

Abstract

We approximate a fuzzy almost quadratic function by a quadratic function in a fuzzy sense. More precisely, we establish a fuzzy Hyers--Ulam--Rassias stability of the quadratic functional equation $f(x+y)+f(x-y)=2f(x)+2f(y)$. Our result can be regarded as a generalization of the stability phenomenon in the framework of normed spaces. We also prove a generalized version of fuzzy stability of the Pexiderized quadratic functional equation $f(x+y)+f(x-y)=2g(x)+2h(y)$.