International Journal of Nonlinear Analysis and Applications
Function weighted $\mathcal{G}$-metric spaces and Hausdorff $\Delta$-distances; an application to fixed point theory
Document Type : Research Paper
Authors
Department of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran
Abstract
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.
Keywords
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Volume 12, Issue 2
November 2021Pages 1441-1452
- Receive Date: 03 June 2020
- Revise Date: 22 September 2020
- Accept Date: 28 September 2020