Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 12 2 2021 11 01 Function weighted $\mathcal{G}$-metric spaces and Hausdorff $\Delta$-distances; an application to fixed point theory 1441 1452 5259 10.22075/ijnaa.2020.20547.2167 EN Ehsan Lotfali Ghasab Department of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran Hamid Majani Department of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran Journal Article 2020 06 03 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. Function weighted $\mathcal{G}$-metric space Hausdorff $\Delta$-distance coupled coincidence point Common coupled fixed point https://ijnaa.semnan.ac.ir/article_5259_af59e02af75d032b4ed517ef2ab8cd74.pdf