Some Hyperstability Results in Non-Archimedean 2-Banach Space for a σ-Jensen Functional Equation

Rachid ELGhali and Samir Kabbaj ()
Additional contact information
Rachid ELGhali: Faculty of Sciences, University of Ibn Tofail
Samir Kabbaj: Faculty of Sciences, University of Ibn Tofail

A chapter in Approximation and Computation in Science and Engineering, 2022, pp 349-367 from Springer

Abstract: Abstract By combining the two versions of Brzdȩk’s fixed point theorem in non-Archimedean Banach spaces Brzdȩk and Ciepliński (Nonlinear Analy 74:6861–6867, 2011) and that in 2-Banach spaces Brzdȩk and Ciepliński (Acta Math Sci 38(2):377–390, 2018), we will investigate the hyperstability of the following σ-Jensen functional equation: f ( x + y ) + f ( x + σ ( y ) ) = 2 f ( x ) , $$\displaystyle f(x+y)+f(x+\sigma (y))=2f(x), $$ where f : X → Y such that X is a normed space, Y is a non-Archimedean 2-Banach space, and σ is a homomorphism of X. In addition, we prove some interesting corollaries corresponding to some inhomogeneous outcomes and particular cases of our main results in C∗-algebras.

Keywords: Stability; Hyperstability; Fixed point theorem; Jensen functional equation; Non-archimedean 2-Banach space; C∗-algebra; Primary: 39B82; Secondary: 39B62, 47H14, 47J20, 47H10 (search for similar items in EconPapers)
Date: 2022
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-030-84122-5_19

Ordering information: This item can be ordered from
http://www.springer.com/9783030841225

DOI: 10.1007/978-3-030-84122-5_19

Access Statistics for this chapter

More chapters in Springer Optimization and Its Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().