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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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.

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

First available in Project Euclid: 19 December 2014

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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

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


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.

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