A fixed point approach to the stability of functional equations in non-Archimedean metric spaces

被引：109

作者：

BrzdeK, Janusz ^{[1
]}

Cieplinski, Krzysztof ^{[1
]}

机构：

[1] Pedag Univ, Dept Math, PL-30084 Krakow, Poland

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2011年 / 74卷 / 18期

关键词：

Non-Archimedean normed space; Ultrametric; Fixed point; Hyers-Ulam stability; Functional equation in a single variable; Metric space; HYERS-ULAM STABILITY; ADDITIVE MAPPINGS; LINEAR RECURRENCE; NORMED SPACES; FIELDS;

D O I：

10.1016/j.na.2011.06.050

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this note, we prove a simple fixed point theorem for a special class of complete metric spaces (namely, complete non-Archimedean metric spaces which are connected with some problems coming from quantum physics, p-adic strings and superstrings). We also show that this theorem is a very efficient and convenient tool for proving the Hyers-Ulam stability of a quite wide class of functional equations in a single variable. (C) 2011 Elsevier Ltd. All rights reserved.

引用

页码：6861 / 6867

页数：7

共 50 条

[1] A fixed point approach to the stability of nonic functional equation in non-Archimedean spaces
Xu, Tian-Zhou
Ding, Yali
Rassias, John Michael
JOURNAL OF COMPUTATIONAL ANALYSIS AND APPLICATIONS, 2017, 22 (02) : 359 - 368
[2] A FIXED POINT APPROACH TO THE STABILITY OF EULER-LAGRANGE SEXTIC (a, b)-FUNCTIONAL EQUATIONS IN ARCHIMEDEAN AND NON-ARCHIMEDEAN BANACH SPACES
Ghaemi, Mohammad Bagher
Choubin, Mehdi
Saadati, Reza
Park, Choonkil
Shin, Dong Yun
JOURNAL OF COMPUTATIONAL ANALYSIS AND APPLICATIONS, 2016, 21 (01) : 170 - 181
[3] STABILITY OF FUNCTIONAL EQUATIONS IN NON-ARCHIMEDEAN SPACES
Moslehian, Mohammad Sal
Rassias, Themistocles M.
APPLICABLE ANALYSIS AND DISCRETE MATHEMATICS, 2007, 1 (02) : 325 - 334
[4] Fixed Point Approach: Ulam Stability Results of Functional Equation in Non-Archimedean Fuzzy ?-2-Normed Spaces and Non-Archimedean Banach Spaces
Tamilvanan, Kandhasamy
Alkhaldi, Ali H.
Agarwal, Ravi P.
Alanazi, Abdulaziz M.
MATHEMATICS, 2023, 11 (02)
[5] STABILITY OF DRYGAS TYPE FUNCTIONAL EQUATIONS WITH INVOLUTION IN NON-ARCHIMEDEAN BANACH SPACES BY FIXED POINT METHOD
Kim, Chang Il
Han, Gil Jun
JOURNAL OF APPLIED MATHEMATICS & INFORMATICS, 2016, 34 (5-6): : 509 - 517
[6] On Ulam Stability of Functional Equations in Non-Archimedean Spaces
Cieplinski, Krzysztof
SYMMETRY-BASEL, 2025, 17 (01):
[7] (JCLR) property and fixed point in non-Archimedean fuzzy metric spaces
Beg, I.
Ahmed, M. A.
Nafadi, H. A.
INTERNATIONAL JOURNAL OF NONLINEAR ANALYSIS AND APPLICATIONS, 2018, 9 (01): : 195 - 201
[8] Fixed point approach to the stability of a cubic and quartic mixed type functional equation in non-archimedean spaces
Elumalai, P.
Sangeetha, S.
Selvan, A. Ponmana
JOURNAL OF MATHEMATICS AND COMPUTER SCIENCE-JMCS, 2024, 33 (02): : 124 - 136
[9] A Fixed Point Approach to Non-Archimedean Stabilities of IQD and IQA Functional Equations
Kumar, Beri Venkatachalapathy Senthil
Sabarinathan, Sriramulu
THAI JOURNAL OF MATHEMATICS, 2022, 20 (01): : 69 - 78
[10] Fixed point theoreins and the Ulam-Hyers stability in non-Archimedean cone metric spaces
Nguyen Bich Huy
Tran Dinh Thanh
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2014, 414 (01) : 10 - 20

← 1 2 3 4 5 →