Approximate Generalized Jensen Mappings in 2-Banach Spaces

Muaadh Almahalebi, Themistocles M. Rassias, Sadeq Al-Ali and Mustapha E. Hryrou
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Muaadh Almahalebi: Ibn Tofail University
Themistocles M. Rassias: National Technical University of Athens
Sadeq Al-Ali: Ibn Tofail University
Mustapha E. Hryrou: Ibn Tofail University

A chapter in Approximation and Computation in Science and Engineering, 2022, pp 17-33 from Springer

Abstract: Abstract Our aim is to investigate the generalized Hyers-Ulam-Rassias stability for the following general Jensen functional equation: ∑ k = 0 n − 1 f ( x + b k y ) = n f ( x ) , $$\displaystyle \sum _{k=0}^{n-1} f(x+ b_{k}y)=nf(x), $$ where n ∈ ℕ 2 $$n \in \mathbb {N}_{2}$$ , b k = exp ( 2 i π k n ) $$b_{k}=\exp (\frac {2i\pi k}{n})$$ for 0 ≤ k ≤ n − 1, in 2-Banach spaces by using a new version of Brzdȩk’s fixed point theorem. In addition, we prove some hyperstability results for the considered equation and the general inhomogeneous Jensen equation ∑ k = 0 n − 1 f ( x + b k y ) = n f ( x ) + G ( x , y ) . $$\displaystyle \sum _{k=0}^{n-1} f(x+ b_{k}y)=nf(x)+G(x,y). $$

Date: 2022
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DOI: 10.1007/978-3-030-84122-5_2

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