On n-Tupled Coincidence and Fixed PointResults in Partially Ordered G-Metric Spaces

Deepak Singh, Varsha Chauhan, Vishal Joshi, Surjeet Singh Tomar

Abstract

The notion of $n$-tupled fixed point is inaugurated by Imdad et al. [1] in 2013. In this paper, some $n$-tupled coincidence and common fixed point theorems (for even $n$) are established in partially ordered complete $G$-metric spaces. Presented theorems can not be obtained from the existing theorems in the frame of reference of allied metric spaces and do not reconcile with the remarks of Samet et al. [2] and Jleli et al. [3]. In fact in a note  Agarwal et al. [4] and Asadi et al. \cite{les20}, recommended new statements to which the technique used in [2, 3] were not applicable. Our results, unify, generalize and extend various known results from the current literature. Also, an example is presented to show the validity of the hypotheses of our results and to distinguish them from the existing ones.