English

Fuzzy almost quadratic functions

Functional Analysis 2021-07-23 v1

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(xy)=2f(x)+2f(y)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(xy)=2g(x)+2h(y)f(x+y)+f(x-y)=2g(x)+2h(y).

Keywords

Cite

@article{arxiv.0710.0106,
  title  = {Fuzzy almost quadratic functions},
  author = {A. K. Mirmostafaee and M. S. Moslehian},
  journal= {arXiv preprint arXiv:0710.0106},
  year   = {2021}
}

Comments

17 pages

R2 v1 2026-06-21T09:24:04.840Z