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Tuyển tập các báo cáo nghiên cứu về hóa học được đăng trên tạp chí hóa hoc quốc tế đề tài : A minimax inequality and its applications to fixed point theorems in CAT(0) spaces | Shabanian and Vaezpour Fixed Point Theory and Applications 2011 2011 61 http www.fixedpointtheoryandapplications.eom content 2011 1 61 Fixed Point Theory and Applications a SpringerOpen Journal RESEARCH Open Access A minimax inequality and its applications to fixed point theorems in CAT 0 spaces S Shabanian and SM Vaezpour Correspondence vaez@aut.ac.ir Department of Mathematics and Computer Science Amirkabir University of Technology Hafez Ave. P.O. Box 15875-4413 Tehran Iran Springer Abstract In this paper a CAT 0 version of famous Fan s minimax inequality is established and as its application we obtain some fixed point theorems and best approximation theorems in CAT 0 spaces. 2000 Mathematics Subject Classification 47H10. Keywords CAT 0 space minimax inequality fixed point 1 Introduction A metric space is a CAT 0 space if it is geodesically connected and if every geodesic triangle in this space is at least as thin as its comparison triangle in Euclidean plane. CAT 0 spaces play fundamental role in various areas of mathematics 1 . Moreover there are applications in biology and computer science as well 2 3 . Fixed point theory in a CAT 0 space was first studied by Kirk 4 . Since then the fixed point theory for single valued and multivalued mappings in CAT 0 spaces has been developed 5-8 . The famous Knaster-Kuratowski-Mazurkiewicz theorem in short KKM theorem and its generalization have a fundamental importance in modern nonlinear analysis 9 10 . Recently Niculescu and Roventa established the KKM mapping principle for CAT 0 spaces 11 . In this paper a minimax inequality in CAT 0 spaces is established and as its application some fixed point and best approximation theorems in CAT 0 spaces are proved. 2 Preliminaries Let X d be a metric space. A geodesic path joining x e X to y e Y briefly a geodesic from x to y is a map c from a closed interval 0 l R to X such that c 0 x c l y and d c t c t t - t for all t t e 0 l . In particular c is an isometry and d x y l. The .
