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Báo cáo hóa học: " Banach operator pairs and common fixed points in modular function spaces"

Tuyển tập các báo cáo nghiên cứu về hóa học được đăng trên tạp chí sinh học đề tài : Banach operator pairs and common fixed points in modular function spaces | Hussain et al. Fixed Point Theory and Applications 2011 2011 75 http www.fixedpointtheoryandapplications.eom content 2011 1 75 Fixed Point Theory and Applications a SpringerOpen Journal RESEARCH Open Access Banach operator pairs and common fixed points in modular function spaces N Hussain 1 MA Khamsi2 and A Latif1 Correspondence alatif@kau.edu. sa department of Mathematics King Abdulaziz University P.O. Box 80203 Jeddah 21589 Saudi Arabia Full list of author information is available at the end of the article Springer Abstract In this article we introduce the concept of a Banach operator pair in the setting of modular function spaces. We prove some common fixed point results for such type of operators satisfying a more general condition of nonexpansiveness. We also establish a version of the well-known De Marr s theorem for an arbitrary family of symmetric Banach operator pairs in modular function spaces without A2-condition. MSC 2000 primary 06F30 47H09 secondary 46B20 47E10 47H10. Keywords Banach operator pair fixed point modular function space nearest point projection asymptotically pointwise p-nonexpansive mapping 1. Introduction The purpose of this article is to give an outline of fixed point theory for mappings defined on some subsets of modular function spaces which are natural generalization of both function and sequence variants of many important from applications perspective spaces like Lebesgue Orlicz Musielak-Orlicz Lorentz Orlicz-Lorentz Calderon-Lozanovskii spaces and many others. This article operates within the framework of convex function modulars. The importance of applications of nonexpansive mappings in modular function spaces lies in the richness of structure of modular function spaces that besides being Banach spaces or F-spaces in a more general settings are equipped with modular equivalents of norm or metric notions and also are equipped with almost everywhere convergence and convergence in submeasure. In many cases particularly in .