×

zbMATH — the first resource for mathematics

Generalized hyperstability of the Jensen functional equation in ultrametric spaces. (English) Zbl 1394.39026
The author investigates some generalized hyperstability results for the Jensen functional equation \[ 2f\left(\frac{x+y}{2}\right)=f(x)+f(y) \] in ultrametric Banach spaces using the fixed point method derived by A. Bahyrycz and M. Piszczek [Acta Math. Hung. 142, No. 2, 353–365 (2014; Zbl 1299.39022)] and J. Brzdęk [Acta Math. Hung. 141, No. 1–2, 58–67 (2013; Zbl 1313.39037); Fixed Point Theory Appl. 2013, Paper No. 285, 9 p. (2013; Zbl 1297.39026)]. The author extends the results found by M. Almahalebi and A. Chahbi [Aequationes Math. 91, No. 4, 647–661 (2017; Zbl 1380.39025)].
MSC:
39B82 Stability, separation, extension, and related topics for functional equations
39B52 Functional equations for functions with more general domains and/or ranges
47H10 Fixed-point theorems
PDF BibTeX Cite
Full Text: DOI
References:
[3] Bahyrycz, A., J. Brzdȩk, and M. Piszczek. 2013. On approximately p-Wright afine functions in ultrametric spaces. Journal of Function Spaces and Applications. (Art. ID 723545). · Zbl 1287.39016
[12] Brzdȩk, J., and K. Ciepliński. 2013. Hyperstability and superstability. Abstract and Applied Analysis 2013. https://doi.org/10.1155/2013/401756. · Zbl 1313.39037
[16] Khrennikov, A. 1997. Non-Archimedean Analysis: Quantum Paradoxes. Dynamical Systems and Biological Models.: Kluwer Academic Publishers, Dordrecht. · Zbl 0920.11087
[20] Ulam, S.M. 1964. Problems in modern mathematics. Science Editions. New York: Wiley. · Zbl 0137.24201
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.