Function weighted \mathcal{G}-metric spaces and Hausdorff \Delta-distances; an application to fixed point theory

In this paper, we introduce a new space which is a generalization of function weighted metric space introduced by Jleli and Samet [On a new generalization of metric spaces, J. Fixed Point Theory Appl. ۲۰۱۸, ۲۰:۱۲۸] where namely function weighted \mathcal{G}-metric space. Also, a Hausdorff \Delta-distance is introduced in these spaces. Then several fixed point results for both single-valued and multi-valued mappings in such spaces are proved. We also construct some examples for the validity of the given results and present an application to the existence of a solution of the Volterra-type integral equation.

Keywords:

Function weighted mathcal{G}-metric space , Hausdorff Delta-distance , coupled coincidence point , Common coupled fixed point