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ON APPROXIMATELY ADDITIVE MAPPINGS IN 2-BANACH SPACES

Part of: Nonlinear operators and their properties

Published online by Cambridge University Press:  15 August 2019

JANUSZ BRZDĘK Open the ORCID record for JANUSZ BRZDĘK [Opens in a new window]  and
EL-SAYED EL-HADY Open the ORCID record for EL-SAYED EL-HADY [Opens in a new window]
JANUSZ BRZDĘK*
Affiliation:
Faculty of Applied Mathematics, AGH University of Science and Technology, Mickiewicza 30, 30-059 Kraków, Poland email brzdek@agh.edu.pl
EL-SAYED EL-HADY
Affiliation:
Mathematics Department, College of Science, Jouf University, PO Box 2014, Sakaka, Saudi Arabia Basic Science Department, Faculty of Computers and Informatics, Suez Canal University, Ismailia, 41522, Egypt email elsayed_elhady@ci.suez.edu.eg
*
✉brzdek@agh.edu.pl
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Abstract

We show how some Ulam stability issues can be approached for functions taking values in 2-Banach spaces. We use the example of the well-known Cauchy equation $f(x+y)=f(x)+f(y)$, but we believe that this method can be applied for many other equations. In particular we provide an extension of an earlier stability result that has been motivated by a problem of Th. M. Rassias. The main tool is a recent fixed point theorem in some spaces of functions with values in 2-Banach spaces.

Keywords

Cauchy equationUlam stability2-Banach space2-norm

MSC classification

Primary: 39B82: Stability, separation, extension, and related topics
Secondary: 39B52: Equations for functions with more general domains and/or ranges 47H10: Fixed-point theorems
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 101 , Issue 2 , April 2020 , pp. 299 - 310
Copyright
© 2019 Australian Mathematical Publishing Association Inc.

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