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Demonstratio Mathematica

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Volume 47, Issue 1

Issues

Linear Approximation And Asymptotic Expansion Associated With The System Of Nonlinear Functional Equations

Le Thi Phuong Ngoc / Huynh Thi Hoang Dung
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  • DEPARTMENT OF MATHEMATICS UNIVERSITY OF ARCHITECTURE OF HO CHI MINH CITY 196 Pasteur Str., Dist. 3 HO CHI MINH CITY, VIETNAM
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/ Pham Hong Danh
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  • DEPARTMENT OF MATHEMATICS STATISTICS AND INFORMATICS UNIVERSITY OF ECONOMICS OF HO CHI MINH CITY 59C Nguyen Dinh Chieu Str., Dist. 3 HO CHI MINH CITY, VIETNAM
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/ Nguyen Thanh Long
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  • DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE UNIVERSITY OF NATURAL SCIENCE VIETNAM NATIONAL UNIVERSITY HO CHI MINH CITY 227 Nguyen Van Cu Str., Dist. 5 HO CHI MINH CITY, VIETNAM
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Published Online: 2014-03-07 | DOI: https://doi.org/10.2478/dema-2014-0008

Abstract

This paper is devoted to the study of the following perturbed system of nonlinear functional equations x ∊Ω=[-b,b], i = 1,…., n; where ε is a small parameter, aijk; bijk are the given real constants, Rijk, Sijk , Xijk : Ω → Ω ,gi → Ω →ℝ , Ψ: Ω x ℝ2→ ℝ are the given continuous functions and ƒi :Ω →ℝ are unknown functions. First, by using the Banach fixed point theorem, we find sufficient conditions for the unique existence and stability of a solution of (E). Next, in the case of Ψ ∊ C2(Ω x ℝ2; ℝ); we investigate the quadratic convergence of (E). Finally, in the case of Ψ ∊ CN(Ω x ℝ2; ℝ) and ε sufficiently small, we establish an asymptotic expansion of the solution of (E) up to order N + 1 in ε. In order to illustrate the results obtained, some examples are also given

Keywords: system of nonlinear functional equations; converges quadratically; perturbed problem; asymptotic expansion

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About the article

Published Online: 2014-03-07

Published in Print: 2014-03-01


Citation Information: Demonstratio Mathematica, Volume 47, Issue 1, Pages 103–124, ISSN (Online) 2391-4661, ISSN (Print) 0420-1213, DOI: https://doi.org/10.2478/dema-2014-0008.

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