tailieunhanh - Báo cáo hóa học: " Fixed point theorems for multivalued maps in cone metric spaces"

Tuyển tập các báo cáo nghiên cứu về hóa học được đăng trên tạp chí hóa hoc quốc tế đề tài : Fixed point theorems for multivalued maps in cone metric spaces | Cho and Bae Fixed Point Theory and Applications 2011 2011 87 http content 2011 1 87 Fixed Point Theory and Applications a SpringerOpen Journal REVIEW Open Access Fixed point theorems for multivalued maps in cone metric spaces Seong-Hoon Cho 1 and Jong-Sook Bae2 Correspondence shcho@hanseo. department of Mathematics Hanseo University Chungnam 356706 South Korea Full list of author information is available at the end of the article Springer Abstract The aim of this article is to generalize a result which is obtained by Mizoguchi and Takahashi J. Math. Anal. Appl. 141 177-188 1989 to the case of cone metric spaces. MSC 47H10 54H25. Keywords fixed point multivalued map cone metric space 1 Introduction Banach contraction principle is widely recognized as the source of metric fixed point theory. Also this principle plays an important role in several branches of mathematics. For instance it has been used to study the existence of solutions for nonlinear equations systems of linear equations and linear integral equations and to prove the convergence of algorithms in computational mathematics. Because of its importance for mathematical theory Banach contraction principle has been extended in many direction see 1-8 . Especially the generalizations to multivalued case are immense too see 6 9 10 . Mizoguchi and Takahashi proved the following theorem in 9 . Theorem . Let X d be a complete metric space and let T X 2X be a multivalued map such that Tx is a closed bounded subset of X for all x _ X. If there exists a function f. 0 0 1 such that lim sup v t 1for all t e 0 to r and if H Tx Ty q d x y d x y for all x y e X x y then T has a fixed point in X. Recently in 10 the authors introduced a cone metric space which is a generalization of a metric space. They generalized Banach contraction principle for cone metric spaces. Since then in 11-23 the authors obtained fixed point theorems in cone metric spaces. And the authors 24 25 .