数学物理学报(英文版) ›› 2022, Vol. 42 ›› Issue (4): 1357-1372.doi: 10.1007/s10473-022-0406-3

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

Ravinder Kumar SHARMA, Sumit CHANDOK   

  1. School of Mathematics, Thapar Institute of Engineering and Technology, Patiala, 147004, India
  • 收稿日期:2020-11-30 修回日期:2021-03-29 出版日期:2022-08-25 发布日期:2022-08-23
  • 通讯作者: Sumit CHANDOK,E-mail:sumit.chandok@thapar.edu E-mail:sumit.chandok@thapar.edu

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

Ravinder Kumar SHARMA, Sumit CHANDOK   

  1. School of Mathematics, Thapar Institute of Engineering and Technology, Patiala, 147004, India
  • Received:2020-11-30 Revised:2021-03-29 Online:2022-08-25 Published:2022-08-23
  • Contact: Sumit CHANDOK,E-mail:sumit.chandok@thapar.edu E-mail:sumit.chandok@thapar.edu

摘要: 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.

关键词: Hyperstability, quasi-2-Banach spaces, fixed point, general linear equation

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

中图分类号: 

  • 47H10