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http://dx.doi.org/10.4134/CKMS.c170344

SOME NEW RESULTS ON HYPERSTABILITY OF THE GENERAL LINEAR EQUATION IN (2, β)-BANACH SPACES  

EL-Fassi, Iz-iddine (Department of Mathematics Faculty of Sciences Ibn Tofail University)
Publication Information
Communications of the Korean Mathematical Society / v.33, no.3, 2018 , pp. 901-917 More about this Journal
Abstract
In this paper, we first introduce the notions of (2, ${\beta}$)-Banach spaces and we will reformulate the fixed point theorem [10, Theorem 1] in this space. We also show that this theorem is a very efficient and convenient tool for proving the new hyperstability results of the general linear equation in (2, ${\beta}$)-Banach spaces. Our main results state that, under some weak natural assumptions, functions satisfying the equation approximately (in some sense) must be actually solutions to it. Our results are improvements and generalizations of the main results of Piszczek [34], Brzdęk [6, 7] and Bahyrycz et al. [2] in (2, ${\beta}$)-Banach spaces.
Keywords
hyperstability; general linear equation; fixed point theorem; (2, ${\beta}$)-normed space;
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Times Cited By KSCI : 1  (Citation Analysis)
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