Coupled fixed point results in cone metric spaces for <inline-formula> <graphic file="1687-1812-2011-27-i1.gif"/> </inline-formula>-compatible mappings

• Main Authors: Samet Bessem, Vetro Calogero, Aydi Hassen
• Format: Article
• Language: English
• Published: SpringerOpen 2011-01-01
• Series: Fixed Point Theory and Applications
• Subjects: <inline-formula> <graphic file="1687-1812-2011-27-i1.gif"/> </inline-formula>-compatible mappings; b-coupled coincidence point; b-common coupled fixed point; cone metric space; integral equation
• Online Access: http://www.fixedpointtheoryandapplications.com/content/2011/1/27
• ISSN: 1687-1820; 1687-1812

<p>Abstract</p> <p>In this paper, we introduce the concepts of <inline-formula> <graphic file="1687-1812-2011-27-i1.gif"/> </inline-formula>-compatible mappings, b-coupled coincidence point and b-common coupled fixed point for mappings <it>F</it>, <it>G </it>: <it>X </it>&#215; <it>X </it>&#8594; <it>X</it>, where (<it>X</it>, <it>d</it>) 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. <b>217</b>, 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.</p> <p> <b>2010 Mathematics Subject Classifications</b>: 54H25; 47H10.</p>