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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2009-01-01
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| Series: | Fixed Point Theory and Applications |
| Online Access: | http://www.fixedpointtheoryandapplications.com/content/2009/892691 |
| Summary: | <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> |
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| ISSN: | 1687-1820 1687-1812 |