tailieunhanh - Báo cáo hóa học: " Research Article Convergence of Iterative Sequences for Fixed Point and Variational Inclusion Problems"

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 Convergence of Iterative Sequences for Fixed Point and Variational Inclusion Problems | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2011 Article ID 368137 15 pages doi 2011 368137 Research Article Convergence of Iterative Sequences for Fixed Point and Variational Inclusion Problems Li Yu and Ma Liang School of Management University of Shanghai for Science and Technology Shanghai 200093 China Correspondence should be addressed to Li Yu brucemath@ Received 14 November 2010 Accepted 8 February 2011 Academic Editor Yeol J. Cho Copyright 2011 L. Yu and M. Liang. 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. An iterative process is considered for finding a common element in the fixed point set of a strict pseudocontraction and in the zero set of a nonlinear mapping which is the sum of a maximal monotone operator and an inverse strongly monotone mapping. Strong convergence theorems of common elements are established in real Hilbert spaces. 1. Introduction and Preliminaries Throughout this paper we always assume that H is a real Hilbert space with the inner product and the norm II II. Let C be a nonempty closed convex subset of H and S C C a nonlinear mapping. In this paper we use F S to denote the fixed point set of S. Recall that the mapping S is said to be nonexpansive if Sx - Syll x - y Nx y e C. S is said to be K-strictly pseudocontractive if there exists a constant K e 0 1 such that Sx - Sy 2 x - y 2 k x - Sx - y - Sy 2 Nx y e C. The class of strictly pseudocontractive mappings was introduced by Browder and Petryshyn 1 in 1967. It is easy to see that every nonexpansive mapping is a 0-strictly pseudocontractive mapping. 2 Fixed Point Theory and Applications Let A C H be a mapping. Recall that A is said to be monotone if Ax - Ay x - y 0 x y e C. A is said to be inverse strongly monotone if there exists a constant a 0 such that Ax - Ay x

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