Banach Journal of Mathematical Analysis

Recent developments of the conditional stability of the homomorphism equation

Janusz Brzdęk, Włodzimierz Fechner, Mohammad Sal Moslehian, and Justyna Sikorska

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Abstract

The issue of Ulam's type stability of an equation is understood in the following way: when a mapping which satisfies the equation approximately (in some sense), it is "close" to a solution of it. In this expository paper, we present a survey and a discussion of selected recent results concerning such stability of the equations of homomorphisms, focussing especially on some conditional versions of them.

Article information

Source
Banach J. Math. Anal., Volume 9, Number 3 (2015), 278-326.

Dates
First available in Project Euclid: 19 December 2014

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1419001718

Digital Object Identifier
doi:10.15352/bjma/09-3-20

Mathematical Reviews number (MathSciNet)
MR3296140

Zentralblatt MATH identifier
1312.39031

Subjects
Primary: 46H99: None of the above, but in this section
Secondary: 39B82: Stability, separation, extension, and related topics [See also 46A22] 39B52: Equations for functions with more general domains and/or ranges 39B55: Orthogonal additivity and other conditional equations

Keywords
Hyers--Ulam--Rassias stability orthogonal) Cauchy equation orthogonality restricted domain sandwich technique fixed point method Hyers' sequence invariant mean method

Citation

Brzdęk, Janusz; Fechner, Włodzimierz; Sal Moslehian, Mohammad; Sikorska, Justyna. Recent developments of the conditional stability of the homomorphism equation. Banach J. Math. Anal. 9 (2015), no. 3, 278--326. doi:10.15352/bjma/09-3-20. https://projecteuclid.org/euclid.bjma/1419001718


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