Tbilisi Mathematical Journal

A fixed points approach to stability of the Pexider equation

B. Bouikhalene, E. Elqorachi, and J. M. Rassias

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Abstract

Using the fixed point theorem we establish the Hyers-Ulam-Rassias stability of the generalized Pexider functional equation $$\frac{1}{\mid K\mid}\sum_{k\in K}f(x+k\cdot y)=g(x)+h(y),\;\;x,y\in E$$ from a normed space $E$ into a complete $\beta$-normed space $F$, where $K$ is a finite abelian subgroup of the automorphism group of the group $(E,+)$.

Article information

Source
Tbilisi Math. J., Volume 7, Issue 2 (2014), 95-110.

Dates
Received: 26 October 2014
Accepted: 2 December 2014
First available in Project Euclid: 12 June 2018

Permanent link to this document
https://projecteuclid.org/euclid.tbilisi/1528768980

Digital Object Identifier
doi:10.2478/tmj-2014-0021

Mathematical Reviews number (MathSciNet)
MR3313060

Zentralblatt MATH identifier
1307.39016

Subjects
Primary: 39B82: Stability, separation, extension, and related topics [See also 46A22]
Secondary: 39B52: Equations for functions with more general domains and/or ranges

Keywords
Stability of functional equation fixed point Pexider equation

Citation

Bouikhalene, B.; Elqorachi, E.; Rassias, J. M. A fixed points approach to stability of the Pexider equation. Tbilisi Math. J. 7 (2014), no. 2, 95--110. doi:10.2478/tmj-2014-0021. https://projecteuclid.org/euclid.tbilisi/1528768980


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