Fixed point theorems for set valued mappings in partially ordered \(G\)-metric space (Q482648)

Recently, \textit{I. Beg} and \textit{A. R. Butt} [Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 71, No. 9, 3699--3704 (2009; Zbl 1176.54028)] obtained sufficient conditions for the existence of common fixed point of a set-valued mapping satisfying an implicit relation in a partially ordered metric space. \textit{Z. Mustafa} and \textit{B. Sims} [J. Nonlinear Convex Anal. 7, No. 2, 289--297 (2006; Zbl 1111.54025)] introduced a more appropriate notion of generalized metric space called G-metric spaces. In this paper, the author proves fixed point theorems in partially ordered complete G-metric spaces for a set-valued mapping satisfying an implicit relation.