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Báo cáo hóa học: " Research Article On a Two-Step Algorithm for Hierarchical Fixed Point Problems and Variational Inequalities"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article On a Two-Step Algorithm for Hierarchical Fixed Point Problems and Variational Inequalities | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2009 Article ID 208692 13 pages doi 10.1155 2009 208692 Research Article On a Two-Step Algorithm for Hierarchical Fixed Point Problems and Variational Inequalities Filomena Cianciaruso 1 Giuseppe Marino 1 Luigi Muglia 1 and Yonghong Yao2 1 Dipartimento di Matematica Universita della Calabria 87036 Arcavacata di Rende CS Italy 2 Department of Mathematics Tianjin Polytechnic University Tianjin 300160 China Correspondence should be addressed to Giuseppe Marino gmarino@unical.it Received 5 May 2009 Accepted 12 September 2009 Recommended by Ram U. Verma A common method in solving ill-posed problems is to substitute the original problem by a family of well-posed i.e. with a unique solution regularized problems. We will use this idea to define and study a two-step algorithm to solve hierarchical fixed point problems under different conditions on involved parameters. Copyright 2009 Filomena Cianciaruso et al. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. Introduction and Preliminar Results A common method in solving ill-posed problems is to substitute the original problem by a family of well-posed i.e. with a unique solution regularized problems. We will use this idea to define and study a two-step algorithm to solve hierarchical fixed point problems under different conditions on involved parameters. We will see that choosing appropriate hypotheses on the parameters we will obtain convergence to the solution of well-posed problems. Changing these assumptions we will obtain convergence to one of the solutions of a ill-posed problem. The results are situaded on the lines of research of Byrne 1 Yang and Zhao 2 Moudafi 3 and Yao and Liou 4 . In this paper we consider variational inequalities of the form x e Fix T such that I - S x x -