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2012 Minimum-Norm Fixed Point of Pseudocontractive Mappings
Habtu Zegeye, Naseer Shahzad, Mohammad Ali Alghamdi
Abstr. Appl. Anal. 2012: 1-15 (2012). DOI: 10.1155/2012/926017

Abstract

Let K be a closed convex subset of a real Hilbert space H and let T : K K be a continuous pseudocontractive mapping. Then for β ( 0 , 1 ) and each t ( 0 , 1 ) , there exists a sequence { y t } K satisfying y t = β P K [ ( 1 t ) y t ] + ( 1 β ) T ( y t ) which converges strongly, as t 0 + , to the minimum-norm fixed point of T. Moreover, we provide an explicit iteration process which converges strongly to a minimum-norm fixed point of T provided that T is Lipschitz. Applications are also included. Our theorems improve several results in this direction.

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Habtu Zegeye. Naseer Shahzad. Mohammad Ali Alghamdi. "Minimum-Norm Fixed Point of Pseudocontractive Mappings." Abstr. Appl. Anal. 2012 1 - 15, 2012. https://doi.org/10.1155/2012/926017

Information

Published: 2012
First available in Project Euclid: 28 March 2013

zbMATH: 06116474
MathSciNet: MR2975314
Digital Object Identifier: 10.1155/2012/926017

Rights: Copyright © 2012 Hindawi

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