Strong convergence theorem for relatively nonexpansive mapping and inverse-strongly-monotone mapping in a Banach space

doi:10.1007/s10483-009-0711-y

Applied Mathematics and Mechanics (English Edition) ›› 2009, Vol. 30 ›› Issue (7): 925-932.doi: https://doi.org/10.1007/s10483-009-0711-y

Strong convergence theorem for relatively nonexpansive mapping and inverse-strongly-monotone mapping in a Banach space

刘英

College of Mathematics and Computer, Hebei University, Baoding 071002,Hebei Province, P. R. China

收稿日期:2009-01-21 修回日期:2009-05-22 出版日期:2009-07-01 发布日期:2009-07-01

Strong convergence theorem for relatively nonexpansive mapping and inverse-strongly-monotone mapping in a Banach space

LIU Ying

College of Mathematics and Computer, Hebei University, Baoding 071002,Hebei Province, P. R. China

Received:2009-01-21 Revised:2009-05-22 Online:2009-07-01 Published:2009-07-01

摘要/Abstract

摘要： In this paper, we introduce an iterative sequence for finding a common element of the set of fixed points of a relatively nonexpansive mapping and the set of solutions of the variational inequality for an inverse-strongly-monotone mapping in a Banach space. Then, we show that the sequence converges strongly to a common element of the two sets. Our results improve and extend the corresponding results reported by many others.

关键词: relatively nonexpansive mapping, generalized projection, inverse-stronglymonotone,variational inequality, p-uniformly convex

Abstract: In this paper, we introduce an iterative sequence for finding a common element of the set of fixed points of a relatively nonexpansive mapping and the set of solutions of the variational inequality for an inverse-strongly-monotone mapping in a Banach space. Then, we show that the sequence converges strongly to a common element of the two sets. Our results improve and extend the corresponding results reported by many others.

Key words: relatively nonexpansive mapping, generalized projection, inverse-stronglymonotone,variational inequality, p-uniformly convex

中图分类号:

刘英. Strong convergence theorem for relatively nonexpansive mapping and inverse-strongly-monotone mapping in a Banach space[J]. Applied Mathematics and Mechanics (English Edition), 2009, 30(7): 925-932.

LIU Ying. Strong convergence theorem for relatively nonexpansive mapping and inverse-strongly-monotone mapping in a Banach space[J]. Applied Mathematics and Mechanics (English Edition), 2009, 30(7): 925-932.

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Strong convergence theorem for relatively nonexpansive mapping and inverse-strongly-monotone mapping in a Banach space

Strong convergence theorem for relatively nonexpansive mapping and inverse-strongly-monotone mapping in a Banach space

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