tailieunhanh - Báo cáo hóa học: "Research Article Approximate Fixed Point Theorems for the Class of Almost S-KKMC Mappings in Abstract Convex Uniform Spaces"

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 Approximate Fixed Point Theorems for the Class of Almost S-KKMC Mappings in Abstract Convex Uniform Spaces | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2009 Article ID 791514 7 pages doi 2009 791514 Research Article Approximate Fixed Point Theorems for the Class of Almost S-KKMC Mappings in Abstract Convex Uniform Spaces Tong-Huei Chang Chi-Ming Chen and Yueh-Hung Huang Department of Applied Mathematics National Hsinchu University of Education Hsin-Chu Taiwan Correspondence should be addressed to Chi-Ming Chen ming@ Received 25 February 2009 Accepted 11 June 2009 Recommended by Hichem Ben-El-Mechaiekh We use a concept of abstract convexity to define the almost S-KKMC property al-S-KKMC X Y family and almost -spaces. We get some new approximate fixed point theorems and fixed point theorems in almost -spaces. Our results extend some results of other authors. Copyright 2009 Tong-Huei Chang et al. 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 and Preliminaries In 1929 Knaster et al. 1 proved the well-known KKM theorem for an n-simplex. Ky Fan s generalization of the KKM theorem to infinite dimensional topological vector spaces in 1961 2 proved to be a very versatile tool in modern nonlinear analysis with many far-reaching applications. Chang and Yen 3 undertook a systematic study of the KKM property and Chang et al. 4 generalized this property as well as the notion of a KKM X Y family of 4 to the wider concepts of the S-KKM property and its related S-KKM X Y Z family. Among the many contributions in the study of the KKM property and related topics we mention the work by Amini et al. 5 where the classes of KKM and S-KKM mappings have been introduced in the framework of abstract convex spaces. The authors of 5 also define a concept of convexity that contains a number of other concepts of abstract convexities and obtain fixed point theorems for .