Iterative algorithms for hierarchical fixed points problems and variational inequalities

Authors:
Yonghong Yao;Yeol Je Cho;Yeong-Cheng Liou
Affiliations:
Department of Mathematics, Tianjin Polytechnic University, Tianjin 300160, China;Department of Mathematics Education and The RINS, Gyeongsang National University, Chinju 660-701, Korea;Department of Information Management, Cheng Shiu University, Kaohsiung 833, Taiwan
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2010

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Abstract

This paper deals with a method for approximating a solution of the fixed point problem: find x@?@?H; x@?=(proj"F"("T")@?S)x@?, where H is a Hilbert space, S is some nonlinear operator and T is a nonexpansive mapping on a closed convex subset C and proj"F"("T") denotes the metric projection on the set of fixed points of T. First, we prove a strong convergence theorem by using a projection method which solves some variational inequality. As a special case, this projection method also solves some minimization problems. Secondly, under different restrictions on parameters, we obtain another strong convergence result which solves the above fixed point problem.