THE GENERALIZED HYPERSTABILITY OF GENERAL LINEAR EQUATION IN QUASI-2-BANACH SPACE

doi:10.1007/s10473-022-0406-3

Abstract

Abstract: In this paper, we study the hyperstability for the general linear equation \[f(ax+by)=Af(x)+Bf(y) \] in the setting of complete quasi-2-Banach spaces. We first extend the main fixed point result of Brzdȩk and Ciepliński (Acta Mathematica Scientia, 2018, ${\bf 38B}$(2): 377-390) to quasi-2-Banach spaces by defining an equivalent quasi-2-Banach space. Then we use this result to generalize the main results on the hyperstability for the general linear equation in quasi-2-Banach spaces. Our results improve and generalize many results of literature.

Key words: Hyperstability, quasi-2-Banach spaces, fixed point, general linear equation

CLC Number:

47H10

Ravinder Kumar SHARMA, Sumit CHANDOK. THE GENERALIZED HYPERSTABILITY OF GENERAL LINEAR EQUATION IN QUASI-2-BANACH SPACE[J].Acta mathematica scientia,Series B, 2022, 42(4): 1357-1372.

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