Stability of a General Functional Equation in m-Banach Spaces

被引：4

作者：

Cieplinski, Krzysztof ^{[1
]}

机构：

[1] AGH Univ Sci & Technol, Fac Appl Math, Mickiewicza 30, PL-30059 Krakow, Poland

来源：

BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY | 2023年 / 46卷 / 02期

关键词：

Ulam stability; Functional equation; Multi-quadratic mapping; m-Banach space; HYERS-ULAM STABILITY;

D O I：

10.1007/s40840-022-01458-y

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this note, the Ulam stability of a general functional equation in several variables is investigated. It is shown that this equation is Ulam stable in m-Banach spaces. Since a particular case of the considered equation is, among others, a functional equation introduced by Ji et al. and Zhao et al. for a characterization of the so-called multi-quadratic mapping, a result on its stability is also presented. Moreover, some other applications are provided.

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页数：11

相关论文

共 26 条

[1] On Ulam Stability of a Linear Difference Equation in Banach Spaces [J].

Baias, Alina Ramona ;

Popa, Dorian .

BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, 2020, 43 (02) :1357-1371

[2] STABILITY AND INVARIANT RANDOM SUBGROUPS [J].

Becker, Oren ;

Lubotzky, Alexander ;

Thom, Andreas .

DUKE MATHEMATICAL JOURNAL, 2019, 168 (12) :2207-2234

[3]

Brzdek J., 2018, Ulam Stability of Operators

[4] A fixed point theorem in n-Banach spaces and Ulam stability [J].

Brzdek, Janusz ;

Cieplinski, Krzysztof .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2019, 470 (01) :632-646

[5] Characterizations on isometries in linear n-normed spaces [J].

Chen, Xiao Yun ;

Song, Mei Mei .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2010, 72 (3-4) :1895-1901

[6] Set-valued solutions of a functional equation [J].

Cieplinski, Krzysztof .

BOLETIN DE LA SOCIEDAD MATEMATICA MEXICANA, 2022, 28 (02)

[7] On perturbations of two general equations in several variables [J].

Cieplinski, Krzysztof .

MATHEMATISCHE ANNALEN, 2023, 385 (1-2) :921-937

[8] Ulam stability of functional equations in 2-Banach spaces via the fixed point method [J].

Cieplinski, Krzysztof .

JOURNAL OF FIXED POINT THEORY AND APPLICATIONS, 2021, 23 (03)

[9] On Ulam Stability of a Functional Equation [J].

Cieplinski, Krzysztof .

RESULTS IN MATHEMATICS, 2020, 75 (04)

[10] Ulam Stability of a Functional Equation in Various Normed Spaces [J].

Cieplinski, Krzysztof .

SYMMETRY-BASEL, 2020, 12 (07)