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 On Some Geometric Constants and the Fixed Point Property for Multivalued Nonexpansive Mappings | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2010 Article ID 596952 12 pages doi 2010 596952 Research Article On Some Geometric Constants and the Fixed Point Property for Multivalued Nonexpansive Mappings Jingxin Zhang1 and Yunan Cui2 1 Department of Mathematics Harbin Institute of Technology Harbin 150001 China 2 Department of Mathematics Harbin University of Science and Technology Harbin 150080 China Correspondence should be addressed to Jingxin Zhang zhjxJ9@ Received 30 July 2010 Accepted 5 October 2010 Academic Editor L. Gorniewicz Copyright 2010 J. Zhang and Y. Cui. 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. We show some geometric conditions on a Banach space X concerning the Jordan-von Neumann constant Zbaganu constant characteristic of separation noncompact convexity and the coefficient R 1 X the weakly convergent sequence coefficient which imply the existence of fixed points for multivalued nonexpansive mappings. 1. Introduction Fixed point theory for multivalued mappings has many useful applications in Applied Sciences in particular in game theory and mathematical economics. Thus it is natural to try of extending the known fixed point results for single-valued mappings to the setting of multivalued mappings. In 1969 Nadler 1 established the multivalued version of Banach s contraction principle. One of the most celebrated results about multivalued mappings was given by Lim 2 in 1974. Using Edelstein s method of asymptotic centers he proved the existence of a fixed point for a multivalued nonexpansive self-mapping T C K C where C is a nonempty bounded closed convex subset of a uniformly convex Banach space. Since then the metric fixed point theory of multivalued mappings has been rapidly developed. Some other classical fixed point theorems for .
