Home OALib Journal OALib PrePrints Submit Ranking News My Lib FAQ About Us Follow Us+
 All Title Author Keywords Abstract
 Publish in OALib Journal ISSN: 2333-9721 APC: Only \$99

 Relative Articles Fixed Points for Multivalued Mappings and the Metric Completeness Fixed Points for Multivalued Mappings in Uniformly Convex Metric Spaces Fixed-Point Theorems for Multivalued Mappings in Modular Metric Spaces Related fixed points for set valued mappings on two metric spaces On common fixed points of pairs of a single and a multivalued coincidentally commuting mappings in -metric spaces Tripled Fixed Points of Multivalued Nonlinear Contraction Mappings in Partially Ordered Metric Spaces On fixed points of multivalued mappings Fixed Point Theorem on Multi-valued Mappings Common Fixed Point Result of Multivalued and Singlevalued Mappings in Partially Ordered Metric Space Fixed Points of Single- and Set-Valued Mappings in Uniformly Convex Metric Spaces with No Metric Convexity More...

# Common Fixed Points for Multivalued Mappings in Complex Valued Metric Spaces with Applications

 Full-Text   Cite this paper

Abstract:

In this paper, we introduce the notion of multivalued contractive mappings in complex valued metric space and prove common fixed point theorems for two multivalued contractive mappings in complex valued metric spaces without using the notion of continuity. Our results improve and extend the results of Azam et al. (2011). 1. Introduction The Banach fixed point theorem was used to establish the existence of a unique solution for a nonlinear integral equation [1]. Moreover, this theorem plays an important role in several branches of mathematics. For instance, it has been used to show the existence of solutions of nonlinear Volterra integral equations and nonlinear integrodifferential equations in the Banach spaces and to show the convergence of algorithms in computational mathematics. Because of its importance and usefulness for mathematical theory, it has become a very popular tool of mathematical analysis in many directions. Nadler [2] introduced the concept of multivalued contraction mappings and obtained the fixed points results for multivalued mappings. Huang and Zhang [3] introduced the notion of cone metric space which is a generalization of metric spaces. They extended Banach contraction principle to cone metric spaces. Since then, Arshad et al. [4], Azam and Arshad [5], Latif and Shaddad [6], Karap？nar [7], and many others obtained fixed point theorems in cone metric spaces (see [8]). The fixed point results regarding rational contractive conditions cannot be extended in cone metric spaces. Azam et al. [9] introduced the concept of complex valued metric spaces and obtained sufficient conditions for the existence of common fixed points of a pair of mappings satisfying contractive type condition involving rational inequalities. In the same way, Rouzkard and Imdad [10] established some common fixed point theorems satisfying certain rational expressions in complex valued metric spaces which generalize, unify, and complement the results of Azam et al. [9]. Recently, Sintunavarat and Kumam [11] obtained common fixed point results by replacing constant of contractive condition with control functions. For more details in the subject, we refer to [12–19]. The aim of this paper is to extend the results of Azam et al. [9] to multivalued mappings in complex valued metric spaces. 2. Preliminaries Let be the set of complex numbers and . Define a partial order on as follows: It follows that if one of the following conditions is satisfied: In particular, we will write if and one of (i), (ii), and (iii) is satisfied and we will write if only (iii) is satisfied.

Full-Text