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Tuyển tập các báo cáo nghiên cứu về hóa học được đăng trên tạp chí hóa hoc quốc tế đề tài : Mixed monotone-generalized contractions in partially ordered probabilistic metric spaces | ứric et al. Fixed Point Theory and Applications 2011 2011 56 http www.fixedpointtheoryandapplications.eom content 2011 1 56 Fixed Point Theory and Applications a SpringerOpen Journal RESEARCH Open Access Mixed monotone-generalized contractions in partially ordered probabilistic metric spaces Ljubomir Ciric 1 Ravi P Agarwal2 and Bessem Samet3 Correspondence agarwal@fit.edu 2Department of Mathematical Sciences Florida Institute of Technology Melbourne FL 32901 USA Full list of author information is available at the end of the article Springer Abstract In this article a new concept of mixed monotone-generalized contraction in partially ordered probabilistic metric spaces is introduced and some coupled coincidence and coupled fixed point theorems are proved. The theorems Presented are an extension of many existing results in the literature and include several recent developments. Mathematics Subject Classification Primary 54H25 Secondary 47H10. Keywords probabilistic metric spacemixed monotone property partially ordered set coupled coincidence fixed point coupled fixed point 1 Introduction The Banach contraction principle 1 is one of the most celebrated fixed point theorem. Many generalizations of this famous theorem and other important fixed point theorems exist in the literature cf. 2-37 . Ran and Reurings 3 proved the Banach contraction principle in partially ordered metric spaces. Recently Agarwal et al. 2 presented some new fixed point results for monotone and generalized contractive type mappings in partially ordered metric spaces. Bhaskar and Lakshmikantham 4 initiated and proved some new coupled fixed point results for mixed monotone and contraction mappings in partially ordered metric spaces. The main idea in 2-11 involve combining the ideas of iterative technique in the contraction mapping principle with those in the monotone technique. In 3 Ran and Reurings proved the following Banach type principle in partially ordered metric spaces. Theorem 1 Ran and .
