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On Series-Like Iterative Equation with a General Boundary Restriction

Fixed Point Theory and Applications volume 2009, Article number: 892691 (2009) Cite this article

Abstract

By means of Schauder fixed point theorem and Banach contraction principle, we investigate the existence and uniqueness of Lipschitz solutions of the equation

. Moreover, we get that the solution depends continuously on. As a corollary, we investigate the existence and uniqueness of Lipschitz solutions of the series-like iterative equation with a general boundary restriction, where is a given Lipschitz function, and are compact convex subsets of with nonempty interior.

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Authors and Affiliations

  1. Department of Mathematics, Harbin Institute of Technology, Harbin, 150001, China

    Wei Song & Guo-qiu Yang

  2. Department of Applied Mathematics, Dalian University of Technology, Dalian, 116024, China

    Feng-chun Lei

Authors
  1. Wei Song
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  2. Guo-qiu Yang
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  3. Feng-chun Lei
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Correspondence to Wei Song.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Song, W., Yang, Gq. & Lei, Fc. On Series-Like Iterative Equation with a General Boundary Restriction. Fixed Point Theory Appl 2009, 892691 (2009). https://doi.org/10.1155/2009/892691

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  • DOI: https://doi.org/10.1155/2009/892691

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