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

Document Type : Research Paper


Department of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran


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. 2018, 20:128] 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.