Abstract
AbstractBy 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: $$\displaystyle f(x+y)+f(x+\sigma (y))=2f(x), $$ 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.KeywordsStabilityHyperstabilityFixed point theoremJensen functional equationNon-archimedean 2-Banach space C∗-algebraMathematics Subject ClassificationPrimary: 39B82; Secondary: 39B6247H1447J2047H10
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