Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-682212220210701Function weighted $mathcal{G}$-metric spaces and Hausdorff $Delta$-distances; an application to fixed point theory14411452525910.22075/ijnaa.2020.20547.2167ENEhsanLotfali GhasabDepartment of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, IranHamidMajaniDepartment of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran0000-0001-7022-6513Journal Article20200603In 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.https://ijnaa.semnan.ac.ir/article_5259_af59e02af75d032b4ed517ef2ab8cd74.pdf