Báo cáo hóa học: " Research Article On Fixed Points of Maximalizing "

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 Fixed Points of Maximalizing | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2010 Article ID 634109 8 pages doi 2010 634109 Research Article On Fixed Points of Maximalizing Mappings in Posets S. Heikkila Department of Mathematical Sciences University of Oulu . Box 3000 90014 Oulu Finland Correspondence should be addressed to S. Heikkila sheikki@ Received 7 October 2009 Accepted 16 November 2009 Academic Editor Mohamed A. Khamsi Copyright 2010 S. Heikkila. 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 use chain methods to prove fixed point results for maximalizing mappings in posets. Concrete examples are also presented. 1. Introduction According to Bourbaki s fixed point theorem cf. 1 2 a mapping G from a partially ordered set X X into itself has a fixed point if G is extensive that is x G x for all x e X and if every nonempty chain of X has the supremum in X. In 3 Theorem 3 the existence of a fixed point is proved for a mapping G X X which is ascending that is G x y implies G x G y . It is easy to verify that every extensive mapping is ascending. In 4 the existence of a fixed point of G is proved if a G a for some a e X and if G is semi-increasing upward that is G x G y whenever x y and G x y. This property holds for instance if G is ascending or increasing that is G x G y whenever x y. In this paper we prove further generalizations to Bourbaki s fixed point theorem by assuming that a mapping G X X is maximalizing that is G x is a maximal element of x G x for all x e X. Concrete examples of maximalizing mappings G which have or do not have fixed points are presented. Chain methods introduced in 5 6 are used in the proofs. These methods are also compared with three other chain methods. 2. Preliminaries A nonempty set X equipped with a reflexive antisymmetric and transitive relation

Không thể tạo bản xem trước, hãy bấm tải xuống
TÀI LIỆU LIÊN QUAN
TÀI LIỆU MỚI ĐĂNG
Đã phát hiện trình chặn quảng cáo AdBlock
Trang web này phụ thuộc vào doanh thu từ số lần hiển thị quảng cáo để tồn tại. Vui lòng tắt trình chặn quảng cáo của bạn hoặc tạm dừng tính năng chặn quảng cáo cho trang web này.