ON STABILITY OF A FUNCTIONAL EQUATION OF QUADRATIC TYPE

被引：7

作者：

Brzdek, J. ^{[1
]}

Jablonska, E. ^{[2
]}

Moslehian, M. S. ^{[3
]}

Pacho, P. ^{[1
]}

机构：

[1] Pedag Univ, Dept Math, Podchorazych 2, PL-30084 Krakow, Poland

[2] Rzeszow Univ Technol, Dept Math, Powstancow Warszawy 12, PL-35959 Rzeszow, Poland

[3] Ferdowsi Univ Mashhad, Dept Pure Math, POB 1159, Mashhad 91775, Iran

来源：

ACTA MATHEMATICA HUNGARICA | 2016年 / 149卷 / 01期

关键词：

Hyers-Ulam stability; p-Wright convexity; fixed point; quadratic equation; FIXED-POINT APPROACH;

D O I：

10.1007/s10474-016-0602-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove some stability results for the equation Af(px * ry) + Bf(qx * sy) = Cf(x) + Df(y), in the class of functions mapping a groupoid (X, *) into a Banach space Y, where p, q, r, s: X -> X are endomorphisms of the groupoid, and A, B, C, D are fixed scalars. Particular cases of the equation are the equation of the p-Wright affine functions, the additive Cauchy equation, the Jensen equation, the quadratic equation and the general linear equation (in two variables).

引用

页码：160 / 169

页数：10

共 15 条

[1]

[Anonymous], 1998, Stability of Functional Equations in Several Variables

[2] Hyperstability of the Jensen functional equation [J].

Bahyrycz, A. ;

Piszczek, M. .

ACTA MATHEMATICA HUNGARICA, 2014, 142 (02) :353-365

[3] On Approximately p-Wright Affine Functions in Ultrametric Spaces [J].

Bahyrycz, Anna ;

Brzdek, Janusz ;

Piszczek, Magdalena .

JOURNAL OF FUNCTION SPACES AND APPLICATIONS, 2013,

[4] RECENT DEVELOPMENTS OF THE CONDITIONAL STABILITY OF THE HOMOMORPHISM EQUATION [J].

Brzdek, Janusz ;

Fechner, Wlodzimierz ;

Moslehian, Mohammad Sal ;

Sikorska, Justyna .

BANACH JOURNAL OF MATHEMATICAL ANALYSIS, 2015, 9 (03) :278-326

[5] Stability of the equation of the p-Wright affine functions [J].

Brzdek, Janusz .

AEQUATIONES MATHEMATICAE, 2013, 85 (03) :497-503

[6] A fixed point approach to stability of functional equations [J].

Brzdek, Janusz ;

Chudziak, Jacek ;

Pales, Zsolt .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2011, 74 (17) :6728-6732

[7] Fixed Points and Generalized Hyers-Ulam Stability [J].

Cadariu, L. ;

Gavruta, L. ;

Gavruta, P. .

ABSTRACT AND APPLIED ANALYSIS, 2012,

[8] APPLICATIONS OF FIXED POINT THEOREMS TO THE HYERS - ULAM STABILITY OF FUNCTIONAL EQUATIONS - A SURVEY [J].

Cieplinski, Krzysztof .

ANNALS OF FUNCTIONAL ANALYSIS, 2012, 3 (01) :151-164

[9] Functional equations involving means [J].

Daroczy, Z. ;

Lajko, K. ;

Lovas, R. L. ;

Maksa, G. Y. ;

Pales, Z. S. .

ACTA MATHEMATICA HUNGARICA, 2007, 116 (1-2) :79-87

[10]

Daróczy Z, 2006, P AM MATH SOC, V134, P521

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