Báo cáo sinh học: A modified Mann iterative scheme by generalized f-projection for a countable family of relatively quasi-nonexpansive mappings and a system of generalized mixed equilibrium 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: A modified Mann iterative scheme by generalized f-projection for a countable family of relatively quasi-nonexpansive mappings and a system of generalized mixed equilibrium problems
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Báo cáo sinh học: "A modified Mann iterative scheme by generalized f-projection for a countable family of relatively quasi-nonexpansive mappings and a system of generalized mixed equilibrium problems"Fixed Point Theory andApplications This Provisional PDF corresponds to the article as it appeared upon acceptance. Fully formatted PDF and full text (HTML) versions will be made available soon. A modified Mann iterative scheme by generalized f-projection for a countablefamily of relatively quasi-nonexpansive mappings and a system of generalized mixed equilibrium problems Fixed Point Theory and Applications 2011, 2011:104 doi:10.1186/1687-1812-2011-104 Siwaporn Saewan (si_wa_pon@hotmail.com) Poom Kumam (poom.kum@kmutt.ac.th) ISSN 1687-1812 Article type Research Submission date 23 July 2011 Acceptance date 21 December 2011 Publication date 21 December 2011 Article URL http://www.fixedpointtheoryandapplications.com/content/2011/1/104 This peer-reviewed article was published immediately upon acceptance. It can be downloaded, printed and distributed freely for any purposes (see copyright notice below). For information about publishing your research in Fixed Point Theory and Applications go to http://www.fixedpointtheoryandapplications.com/authors/instructions/ For information about other SpringerOpen publications go to http://www.springeropen.com © 2011 Saewan and Kumam ; licensee Springer.This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.A modified Mann iterative scheme by generalized f -projection for a countable family of relatively quasi-nonexpansive mappings and a system of generalized mixed equilibrium problems Siwaporn Saewan∗1 and Poom Kumam∗1,2 1 Department of Mathematics, Faculty of ScienceKing Mongkut’s University of Technology Thonburi (KMUTT) Bangmod, Bangkok 10140, Thailand 2 Centre of Excellence in Mathematics, CHE Si Ayutthaya Rd., Bangkok 10400, Thailand ∗ Corresponding authors: si wa pon@hotmail.com Email address: PK: kumampoom@hotmail.com; poom.kum@kmutt.ac.th Abstract The purpose of this paper is to introduce a new hybrid projection method based on modified Mann iterative scheme by the general- ized f -projection operator for a countable family of relatively quasi- nonexpansive mappings and the solutions of the system of generalized mixed equilibrium problems. Furthermore, we prove the strong con- vergence theorem for a countable family of relatively quasi-nonexpansive mappings in a uniformly convex and uniform smooth Banach space. Finally, we also apply our results to the problem of finding zeros of B -monotone mappings and maximal monotone operators. The results 1 presented in this paper generalize and improve some well-known re- sults in the literature. Keywords: The generalized f -projection operator; relatively quasi- nonexpansive mapping; B-monotone mappings; maximal monotone operator; system of generalized mixed equilibrium problems. 2000 Mathematics Subject Classification: 47H05; 47H09; 47H10.1 IntroductionThe theory of equilibrium problems, the development of an efficient and im-plementable iterative algorithm, is interesting and important. This theorycombines theoretical and algorithmic advances with novel domain of applica-tions. Analysis of these problems requires a blend of techniques from convexanalysis, functional analysis, and numerical analysis. Equilibrium problems theory provides us with a natural, novel, and uni-fied framework for studying a wide class of problems arising in economics,finance, transportation, network, and structural analysis, image reconstruc-tion, ecology, elasticity and optimization, and it has been extended and gen-eralized in many directions. The ideas and techniques of this theory are beingused in a variety of diverse areas and proved to be productive and innovative.In particular, generalized mixed equi ...