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 Quasicone Metric Spaces and Generalizations of Caristi Kirk’s Theorem | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2009 Article ID 574387 9 pages doi 2009 574387 Research Article Quasicone Metric Spaces and Generalizations of Caristi Kirk s Theorem Thabet Abdeljawad1 and Erdal Karapinar2 1 Department of Mathematics Cankaya University 06530 Ankara Turkey 2 Department of Mathematics Attltm University 06836 Ankara Turkey Correspondence should be addressed to Thabet Abdeljawad thabet@ Received 4 July 2009 Accepted 3 December 2009 Recommended by Hichem Ben-El-Mechaiekh Cone-valued lower semicontinuous maps are used to generalize Cristi-Kirik s fixed point theorem to Cone metric spaces. The cone under consideration is assumed to be strongly minihedral and normal. First we prove such a type of fixed point theorem in compact cone metric spaces and then generalize to complete cone metric spaces. Some more general results are also obtained in quasicone metric spaces. Copyright 2009 T. Abdeljawad and E. Karapinar. 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 2007 Huang and Zhang 1 introduced the notion of cone metric spaces CMSs by replacing real numbers with an ordering Banach space. The authors there gave an example of a function which is contraction in the category of cone metric spaces but not contraction if considered over metric spaces and hence by proving a fixed point theorem in cone metric spaces ensured that this map must have a unique fixed point. After that series of articles about cone metric spaces started to appear. Some of those articles dealt with the extension of certain fixed point theorems to cone metric spaces see . 2-5 and some other with the structure of the spaces themselves see . 3 6 . Very recently some authors have used regular cones to extend some fixed point .