On approximate solutions of the generalized Volterra integral equation

被引：9

作者：

Bahyrycz, Anna ^{[1
]}

Brzdek, Janusz ^{[1
]}

Lesniak, Zbigniew ^{[1
]}

机构：

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

来源：

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS | 2014年 / 20卷

关键词：

Volterra integral equation; Fixed point; Ulam stability; Approximate solution; Uniqueness; FIXED-POINT APPROACH; STABILITY;

D O I：

10.1016/j.nonrwa.2014.04.004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove some results on approximate solutions of the generalized Volterra integral equation psi(x) = integral(x)(a) N(x, t, psi(alpha(x, t))) dt + G(x) for continuous functions mapping a real interval I, of the form [a, b) or [a, b] or [a, infinity), into a Banach space. We show that, under suitable assumptions, they generate exact solutions of the equation. In particular, we consider the issue of uniqueness of approximate and exact solutions of the equation. (C) 2014 Elsevier Ltd. All rights reserved.

引用

页码：59 / 66

页数：8

共 18 条

[1]

Akkouchi M., 2011, Acta Universitatis Apulensis, V26, P257

[2]

[Anonymous], INTEGRAL EQUATIONS T

[3]

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

[4]

Brillouet-Belluot N., 2012, Abs. Appl. Anal, V2012, DOI [DOI 10.1155/2012/716936, 10.1155/2012/716936]

[5] A fixed point approach to the stability of functional equations in non-Archimedean metric spaces [J].

BrzdeK, Janusz ;

Cieplinski, Krzysztof .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2011, 74 (18) :6861-6867

[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] Hyers-Ulam and Hyers-Ulam-Rassias Stability of Volterra Integral Equations with Delay [J].

Castro, L. P. ;

Ramos, A. .

INTEGRAL METHODS IN SCIENCE AND ENGINEERING, VOL 1: ANALYTIC METHODS, 2010, :85-94

[8]

Corduneanu C., 1991, Integral Equations and Applications, V148

[9]

Corduneanu Constantine., 1971, Principles of Differential and Integral Equations

[10]

Gachpazan M, 2010, INT J NONLINEAR ANAL, V1, P19

← 1 2 →