On Series-Like Iterative Equation with a General Boundary Restriction

On Series-Like Iterative Equation with a General Boundary Restriction

<p>Abstract</p> <p>By means of Schauder fixed point theorem and Banach contraction principle, we investigate the existence and uniqueness of Lipschitz solutions of the equation <graphic file="1687-1812-2009-892691-i1.gif"/>. Moreover, we get that the solution <gr...

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Main Authors: Lei Feng-chun, Song Wei, Yang Guo-qiu
Format: Article
Language:English
Published: SpringerOpen 2009-01-01
Series:Fixed Point Theory and Applications
Online Access:http://www.fixedpointtheoryandapplications.com/content/2009/892691
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spelling doaj-48de1632a5524422b4dd0f239b4fe5c82020-11-25T01:08:07ZengSpringerOpenFixed Point Theory and Applications1687-18201687-18122009-01-0120091892691On Series-Like Iterative Equation with a General Boundary RestrictionLei Feng-chunSong WeiYang Guo-qiu<p>Abstract</p> <p>By means of Schauder fixed point theorem and Banach contraction principle, we investigate the existence and uniqueness of Lipschitz solutions of the equation <graphic file="1687-1812-2009-892691-i1.gif"/>. Moreover, we get that the solution <graphic file="1687-1812-2009-892691-i2.gif"/> depends continuously on <graphic file="1687-1812-2009-892691-i3.gif"/>. As a corollary, we investigate the existence and uniqueness of Lipschitz solutions of the series-like iterative equation <graphic file="1687-1812-2009-892691-i4.gif"/> with a general boundary restriction, where <graphic file="1687-1812-2009-892691-i5.gif"/> is a given Lipschitz function, and <graphic file="1687-1812-2009-892691-i6.gif"/> are compact convex subsets of <graphic file="1687-1812-2009-892691-i7.gif"/> with nonempty interior.</p>http://www.fixedpointtheoryandapplications.com/content/2009/892691
collection DOAJ
language English
format Article
sources DOAJ
author Lei Feng-chun
Song Wei
Yang Guo-qiu
spellingShingle Lei Feng-chun
Song Wei
Yang Guo-qiu
On Series-Like Iterative Equation with a General Boundary Restriction
Fixed Point Theory and Applications
author_facet Lei Feng-chun
Song Wei
Yang Guo-qiu
author_sort Lei Feng-chun
title On Series-Like Iterative Equation with a General Boundary Restriction
title_short On Series-Like Iterative Equation with a General Boundary Restriction
title_full On Series-Like Iterative Equation with a General Boundary Restriction
title_fullStr On Series-Like Iterative Equation with a General Boundary Restriction
title_full_unstemmed On Series-Like Iterative Equation with a General Boundary Restriction
title_sort on series-like iterative equation with a general boundary restriction
publisher SpringerOpen
series Fixed Point Theory and Applications
issn 1687-1820
1687-1812
publishDate 2009-01-01
description <p>Abstract</p> <p>By means of Schauder fixed point theorem and Banach contraction principle, we investigate the existence and uniqueness of Lipschitz solutions of the equation <graphic file="1687-1812-2009-892691-i1.gif"/>. Moreover, we get that the solution <graphic file="1687-1812-2009-892691-i2.gif"/> depends continuously on <graphic file="1687-1812-2009-892691-i3.gif"/>. As a corollary, we investigate the existence and uniqueness of Lipschitz solutions of the series-like iterative equation <graphic file="1687-1812-2009-892691-i4.gif"/> with a general boundary restriction, where <graphic file="1687-1812-2009-892691-i5.gif"/> is a given Lipschitz function, and <graphic file="1687-1812-2009-892691-i6.gif"/> are compact convex subsets of <graphic file="1687-1812-2009-892691-i7.gif"/> with nonempty interior.</p>
url http://www.fixedpointtheoryandapplications.com/content/2009/892691
work_keys_str_mv AT leifengchun onserieslikeiterativeequationwithageneralboundaryrestriction
AT songwei onserieslikeiterativeequationwithageneralboundaryrestriction
AT yangguoqiu onserieslikeiterativeequationwithageneralboundaryrestriction
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