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Báo cáo hóa học: " Coupled fixed point results in cone metric spaces for w-compatible mappings"

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: Coupled fixed point results in cone metric spaces for w-compatible mappings | Aydi et al. Fixed Point Theory and Applications 2011 2011 27 http www.fixedpointtheoryandapplications.eom content 2011 1 27 Fixed Point Theory and Applications a SpringerOpen Journal RESEARCH Open Access Coupled fixed point results in cone metric spaces for íỉ-compatible mappings Hassen Aydi 1 Bessem Samet2 and Calogero Vetro3 Correspondence hassen. aydi@isima.rnu.tn 1Institut Supérieur d lnformatique de Mahdia Université de Monastir Route de Rjiche Km 4 BP 35 Mahdia 5121 Tunisie Full list of author information is available at the end of the article SpringerOpen0 Abstract In this paper we introduce the concepts of w-compatible mappings b-coupled coincidence point and b-common coupled fixed point for mappings F G X X X X where X d is a cone metric space. We establish b-coupled coincidence and b-common coupled fixed point theorems in such spaces. The presented theorems generalize and extend several well-known comparable results in the literature in particular the recent results of Abbas et al. Appl. Math. Comput. 217 195-202 2010 . Some examples are given to illustrate our obtained results. An application to the study of existence of solutions for a system of non-linear integral equations is also considered. 2010 Mathematics Subject Classifications 54H25 47H10. Keywords -compatible mappings b-coupled coincidence point b-common coupled fixed point cone metric space integral equation 1 Introduction Ordered normed spaces and cones have applications in applied mathematics for instance in using Newton s approximation method 1-4 and in optimization theory 5 . K-metric and K-normed spaces were introduced in the mid-20th century 2 see also 3 4 6 by using an ordered Banach space instead of the set of real numbers as the codomain for a metric. Huang and Zhang 7 re-introduced such spaces under the name of cone metric spaces and went further defining convergent and Cauchy sequences in the terms of interior points of the underlying cone. Afterwards many papers about fixed point .