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Báo cáo hóa học: "Strong convergence theorems for variational inequalities and fixed points of a countable family of nonexpansive mappings"

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: Strong convergence theorems for variational inequalities and fixed points of a countable family of nonexpansive mappings | Bunyawat and Suantai Fixed Point Theory and Applications 2011 2011 47 http www.fixedpointtheoryandapplications.eom content 2011 1 47 Fixed Point Theory and Applications a SpringerOpen Journal RESEARCH Open Access Strong convergence theorems for variational inequalities and fixed points of a countable family of nonexpansive mappings Aunyarat Bunyawat1 and Suthep Suantai2 Correspondence scmti005@chiangmai.ac.th 2Centre of Excellence in Mathematics CHE Si Ayutthaya Road Bangkok 10400 Thailand Full list of author information is available at the end of the article Springer Abstract A new general iterative method for finding a common element of the set of solutions of variational inequality and the set of common fixed points of a countable family of nonexpansive mappings is introduced and studied. A strong convergence theorem of the proposed iterative scheme to a common fixed point of a countable family of nonexpansive mappings and a solution of variational inequality of an inverse strongly monotone mapping are established. Moreover we apply our main result to obtain strong convergence theorems for a countable family of nonexpansive mappings and a strictly pseudocontractive mapping and a countable family of uniformly k-strictly pseudocontractive mappings and an inverse strongly monotone mapping. Our main results improve and extend the corresponding result obtained by Klin-eam and Suantai J Inequal Appl 520301 16 pp 2009 . Mathematics Subject Classification 2000 47H09 47H10 Keywords countable family of nonexpansive mappings variational inequality inverse strongly monotone mapping strictly pseudocontractive mapping countable family of uniformly k-strictly pseudocontractive mappings 1 Introduction Let H be a real Hilbert space and C be a nonempty closed convex subset of H. In this paper we always assume that a bounded linear operator A on H is strongly positive that is there is a constant Y 0 such that Ax x Y x 2 for all x e H. Recall that a mapping T of H into itself is .