Asymptotic Stability of the Pexider–Cauchy Functional Equation in Non-Archimedean Spaces

Hamid Gharib, Mohammad B. Moghimi, Abbas Najati and Jae-Hyeong Bae
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Hamid Gharib: Department of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil 56199-11367, Iran
Mohammad B. Moghimi: Department of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil 56199-11367, Iran
Abbas Najati: Department of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil 56199-11367, Iran
Jae-Hyeong Bae: Humanitas College, Kyung Hee University, Yongin 17104, Korea

Mathematics, 2021, vol. 9, issue 18, 1-13

Abstract: In this paper, we investigated the asymptotic stability behaviour of the Pexider–Cauchy functional equation in non-Archimedean spaces. We also showed that, under some conditions, if ? f ( x + y ) ? g ( x ) ? h ( y ) ? ? ? , then f , g and h can be approximated by additive mapping in non-Archimedean normed spaces. Finally, we deal with a functional inequality and its asymptotic behaviour.

Keywords: non-Archimedean space; Pexider–Cauchy equation; asymptotic stability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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