On new stability results for composite functional equations in quasi-β-normed spaces-Reference-Cited by-同舟云学术

On new stability results for composite functional equations in quasi-β-normed spaces

Published:2021-01-01 Issue:1 Volume:54 Page:68-84
ISSN:2391-4661
Container-title:Demonstratio Mathematica
language:en
Short-container-title:

Author:

Thanyacharoen Anurak¹,Sintunavarat Wutiphol²

Affiliation:

1. Department of Mathematics, Faculty of Science and Technology, Muban Chombueng Rajabhat University , Chom Bueng , Ratchaburi, 70150 , Thailand

2. Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University , Phatum Thani 12120 , Thailand

Abstract

Abstract In this article, we prove the generalized Hyers-Ulam-Rassias stability for the following composite functional equation: f ( f ( x ) − f ( y ) ) = f ( x + y ) + f ( x − y ) − f ( x ) − f ( y ) ,

f(f\left(x)-f(y))=f\left(x+y)+f\left(x-y)-f\left(x)-f(y),

where

maps from a

( β , p )

\left(\beta ,p)

-Banach space into itself, by using the fixed point method and the direct method. Also, the generalized Hyers-Ulam-Rassias stability for the composite

-functional inequality is discussed via our results.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/dema-2021-0002/pdf

Reference35 articles.

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3. Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), no. 2, 297–300.

4. P. Gãvruta, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl. 184 (1994), 431–436.

5. S. Gołąb and A. Schinzel, Sur lequation fonctionnelle f(x+f(x)y)=f(x)f(y), Publ. Math. Debrecen 6 (1959), 113–125.

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