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The generalized hyperstability of general linear equations in quasi-Banach spaces

Authors: 
Nguyen Van Dung, Vo Thi Le Hang
Publisher: 
Journal of Mathematical Analysis and Applications
Publication year: 
Abstract: 

In this paper, we study the hyperstability for the general linear equation in the setting of quasi-Banach spaces. We first extend the fixed point result of Brzdek et al. [5, Theorem 1] in metric spaces to b-metric spaces, in particular to quasi-Banach spaces. Then we use this result to generalize the main results on the hyperstability for the general linear equation in Banach spaces to quasi-Banach spaces. We also show that we can not omit the assumption of completeness in [5, Theorem 1]. As a consequence, we conclude that we need more explanations to replace a normed space by its completion in the proofs of some results in the literature.