Document Type : Research Paper


Department of Mathematics, Faculty of Science, Erzurum Technical University, P.O.Box 25050, Erzurum, Turkey.


In this paper, necessary and sufficient conditions for the existence and uniqueness of fixed points of generalized Geraghty type contraction mappings are given in complete partial $b_{v}(s) $-metric spaces. The results are more general than several results that exist in the literature because of the considered space. A numerical example is given to support the obtained results. Also, the existence and uniqueness of the solutions of an integral equation has been verified considered as an application.


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