The Cauchy–Optimal Stability Results for Cauchy–Jensen Additive Mappings in the Fuzzy Banach Space and the Unital Fuzzy Banach Space-Reference-Cited by-同舟云学术

The Cauchy–Optimal Stability Results for Cauchy–Jensen Additive Mappings in the Fuzzy Banach Space and the Unital Fuzzy Banach Space

Published:2023-04-21 Issue:4 Volume:12 Page:405
ISSN:2075-1680
Container-title:Axioms
language:en
Short-container-title:Axioms

Author:

Eidinejad Zahra¹^ORCID,Saadati Reza¹^ORCID,Srivastava Hari M.²³⁴⁵^ORCID

Affiliation:

1. School of Mathematics, Iran University of Science and Technology, Narmak, Tehran 13114-16846, Iran

2. Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 2Y2, Canada

3. Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan

4. Department of Mathematics and Informatics, Azerbaijan University, 71 Jeyhun Hajibeyli Street, AZ1007 Baku, Azerbaijan

5. Center for Converging Humanities, Kyung Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, Seoul 02447, Republic of Korea

Abstract

In this article, we apply a new class of fuzzy control functions to approximate a Cauchy additive mapping in fuzzy Banach space (FBS). Further, considering the unital FBS (UFBS), we will investigate the isomorphisms defined in this space. By introducing several specific functions and choosing the optimal control function from among these functions, we evaluate the Cauchy–Optimal stability (C–O-stability) for all defined mappings.

Publisher

MDPI AG

Subject

Geometry and Topology,Logic,Mathematical Physics,Algebra and Number Theory,Analysis

Link

https://www.mdpi.com/2075-1680/12/4/405/pdf

Reference17 articles.

1. Ulam, S.M. (1960). Problems in Modern Mathematics, Wiley.

2. On the stability of the linear functional equation;Hyers;Proc. Natl. Acad. Sci. USA,1941

3. On the stability of the linear mapping in Banach spaces;Rassias;Proc. Am. Math. Soc.,1978

4. A generalization of the Hyers–Ulam–Rassias stability of approximately additive mappings;J. Math. Anal. Appl.,1994

5. A generalization of the Hyers–Ulam–Rassias stability of Jensen’s equation;Jun;J. Math. Anal. Appl.,1999