ON A FIXED POINT THEOREM IN 2-BANACH SPACES AND SOME OF ITS APPLICATIONS

doi:10.1016/S0252-9602(18)30755-0

数学物理学报(英文版) ›› 2018, Vol. 38 ›› Issue (2): 377-390.doi: 10.1016/S0252-9602(18)30755-0

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ON A FIXED POINT THEOREM IN 2-BANACH SPACES AND SOME OF ITS APPLICATIONS

Janusz BRZD?K¹, Krzysztof CIEPLINSKI²

1. Pedagogical University, Department of Mathematics, Podchor??ych 2, 30-084 Kraków, Poland;
2. AGH University of Science and Technology, Faculty of Applied Mathematics, Mickiewicza 30, 30-059 Kraków, Poland

收稿日期:2016-04-12 修回日期:2017-06-06 出版日期:2018-04-25 发布日期:2018-04-25
通讯作者: Krzysztof CIEPLINSKI E-mail:cieplin@agh.edu.pl
作者简介:Janusz BRZDȨK,E-mail:jbrzdek@up.krakow.pl

ON A FIXED POINT THEOREM IN 2-BANACH SPACES AND SOME OF ITS APPLICATIONS

Janusz BRZD?K¹, Krzysztof CIEPLINSKI²

1. Pedagogical University, Department of Mathematics, Podchor??ych 2, 30-084 Kraków, Poland;
2. AGH University of Science and Technology, Faculty of Applied Mathematics, Mickiewicza 30, 30-059 Kraków, Poland

Received:2016-04-12 Revised:2017-06-06 Online:2018-04-25 Published:2018-04-25
Contact: Krzysztof CIEPLINSKI E-mail:cieplin@agh.edu.pl

摘要/Abstract

摘要：

The aim of this article is to prove a fixed point theorem in 2-Banach spaces and show its applications to the Ulam stability of functional equations. The obtained stability results concern both some single variable equations and the most important functional equation in several variables, namely, the Cauchy equation. Moreover, a few corollaries corresponding to some known hyperstability outcomes are presented.

关键词: fixed point theorem, 2-normed space, Ulam stability, hyperstability

Abstract:

Key words: fixed point theorem, 2-normed space, Ulam stability, hyperstability

Janusz BRZDȨK, Krzysztof CIEPLINSKI. ON A FIXED POINT THEOREM IN 2-BANACH SPACES AND SOME OF ITS APPLICATIONS[J]. 数学物理学报(英文版), 2018, 38(2): 377-390.

Janusz BRZDȨK, Krzysztof CIEPLINSKI. ON A FIXED POINT THEOREM IN 2-BANACH SPACES AND SOME OF ITS APPLICATIONS[J]. Acta mathematica scientia,Series B, 2018, 38(2): 377-390.

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ON A FIXED POINT THEOREM IN 2-BANACH SPACES AND SOME OF ITS APPLICATIONS

ON A FIXED POINT THEOREM IN 2-BANACH SPACES AND SOME OF ITS APPLICATIONS

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