ON NEW APPROXIMATIONS FOR GENERALIZED CAUCHY FUNCTIONAL EQUATIONS USING BRZDȨK AND CIEPLIŃSKI'S FIXED POINT THEOREMS IN 2-BANACH SPACES

doi:10.1007/s10473-020-0316-1

数学物理学报(英文版) ›› 2020, Vol. 40 ›› Issue (3): 824-834.doi: 10.1007/s10473-020-0316-1

ON NEW APPROXIMATIONS FOR GENERALIZED CAUCHY FUNCTIONAL EQUATIONS USING BRZDȨK AND CIEPLIŃSKI'S FIXED POINT THEOREMS IN 2-BANACH SPACES

Laddawan AIEMSOMBOON, Wutiphol SINTUNAVARAT

Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University Rangsit Center, Pathumthani 12121, Thailand

收稿日期:2019-02-11 修回日期:2019-08-29 出版日期:2020-06-25 发布日期:2020-07-17
通讯作者: Wutiphol SINTUNAVARAT E-mail:wutiphol@mathstat.sci.tu.ac.th
作者简介:Laddawan AIEMSOMBOON,E-mail:Laddawan_Aiemsomboon@hotmail.com
基金资助:
This work was supported by Research Professional Development Project under the Science Achievement Scholarship of Thailand (SAST) and Thammasat University Research Fund, Contract No. TUGG 33/2562. The second author would like to thank the Thailand Research Fund and Office of the Higher Education Commission under grant no. MRG6180283 for financial support during the preparation of this manuscript.

ON NEW APPROXIMATIONS FOR GENERALIZED CAUCHY FUNCTIONAL EQUATIONS USING BRZDȨK AND CIEPLIŃSKI'S FIXED POINT THEOREMS IN 2-BANACH SPACES

Laddawan AIEMSOMBOON, Wutiphol SINTUNAVARAT

Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University Rangsit Center, Pathumthani 12121, Thailand

Received:2019-02-11 Revised:2019-08-29 Online:2020-06-25 Published:2020-07-17
Contact: Wutiphol SINTUNAVARAT E-mail:wutiphol@mathstat.sci.tu.ac.th
Supported by:
This work was supported by Research Professional Development Project under the Science Achievement Scholarship of Thailand (SAST) and Thammasat University Research Fund, Contract No. TUGG 33/2562. The second author would like to thank the Thailand Research Fund and Office of the Higher Education Commission under grant no. MRG6180283 for financial support during the preparation of this manuscript.

摘要/Abstract

摘要： In this work, we apply the Brzdȩk and Ciepliński's fixed point theorem to investigate new stability results for the generalized Cauchy functional equation of the form
f(ax + by)=af(x) + bf(y),
where a,b ∈ N and f is a mapping from a commutative group (G, +) to a 2-Banach space (Y,||·,·||). Our results are generalizations of main results of Brzdȩk and Ciepliński[J Brzdȩk, K Ciepliński. On a fixed point theorem in 2-normed spaces and some of its applications. Acta Mathematica Scientia, 2018, 38B(2):377-390].

关键词: Fixed point theorem, generalized Cauchy functional equation, 2-normed space, stability

Abstract: In this work, we apply the Brzdȩk and Ciepliński's fixed point theorem to investigate new stability results for the generalized Cauchy functional equation of the form
f(ax + by)=af(x) + bf(y),
where a,b ∈ N and f is a mapping from a commutative group (G, +) to a 2-Banach space (Y,||·,·||). Our results are generalizations of main results of Brzdȩk and Ciepliński[J Brzdȩk, K Ciepliński. On a fixed point theorem in 2-normed spaces and some of its applications. Acta Mathematica Scientia, 2018, 38B(2):377-390].

Key words: Fixed point theorem, generalized Cauchy functional equation, 2-normed space, stability

中图分类号:

47H10

Laddawan AIEMSOMBOON, Wutiphol SINTUNAVARAT. ON NEW APPROXIMATIONS FOR GENERALIZED CAUCHY FUNCTIONAL EQUATIONS USING BRZDȨK AND CIEPLIŃSKI'S FIXED POINT THEOREMS IN 2-BANACH SPACES[J]. 数学物理学报(英文版), 2020, 40(3): 824-834.

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ON NEW APPROXIMATIONS FOR GENERALIZED CAUCHY FUNCTIONAL EQUATIONS USING BRZDȨK AND CIEPLIŃSKI'S FIXED POINT THEOREMS IN 2-BANACH SPACES

ON NEW APPROXIMATIONS FOR GENERALIZED CAUCHY FUNCTIONAL EQUATIONS USING BRZDȨK AND CIEPLIŃSKI'S FIXED POINT THEOREMS IN 2-BANACH SPACES

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