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 Fixed Point Theorems for Middle Point | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2008 Article ID 648591 13 pages doi 2008 648591 Research Article Fixed Point Theorems for Middle Point Linear Operators in L1 Milena Chermisi1 and Anna Martellotti2 1 Fachbereich Mathematik Universitat Duisburg-Essen Lotharstrafie 65 47057 Duisburg Germany 2 Dipartimento di Matematica e Informatica Universita di Perugia via Vanvitelli 1 06123 Perugia Italy Correspondence should be addressed to Milena Chermisi chermisi@ Received 3 February 2008 Revised 11 August 2008 Accepted 8 September 2008 Recommended by Klaus Schmitt We introduce the notion of middle point linear operators. We prove a fixed point result for middle point linear operators in L1. We then present some examples and as an application we derive a Markov-Kakutani type fixed point result for commuting family of a-nonexpansive and middle point linear operators in L1. Copyright 2008 M. Chermisi and A. Martellotti. 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. 1. Introduction Furi and Vignoli 1 proved that any a-nonexpansive map T K K on a nonempty bounded closed convex subset K of a Banach space X satisfies inf T x - x 0 M xeK where a is the Kuratowski measure of noncompactness on X. It is of great importance to obtain the existence of fixed points for such mappings in many applications such as eigenvalue problems as well as boundary value problems including approximation theory variational inequalities and complementarity problems. Such results are used in applied mathematics engineering and economics. In this paper we give optimal sufficient conditions for T to have a fixed point on K in case that X L1 p where pi is an ơ-finite measure and as a minor application in case that X is a reflexive Banach space. The study of fixed point theory has been .
