Global Best Approximate Solutions for Set Valued Contraction in \(b\)-metric Spaces with Applications

Azhar Hussain, Tanzeela Kanwal, Ahmed Al-Rawashdeh

Abstract


The aim of this paper is to introduce the notion of multivalued Ciric type \(\alpha_{*}\)-\(\psi\)-proximal contraction and prove some best proximity point results for such contraction in \(b\)-metric spaces. We also deduce some best proximity point results for single valued mapping. Moreover, we apply our results to obtain relative best proximity point results in partially ordered metric spaces. As an application of our results we obtain fixed point results for the spaces concern. We give some examples to illustrate the obtained results. Finally, an application to nonlinear integral equation is presented. Our results extended and generalized many existing results in the literature.

Keywords


Best proximity point; Weak P-property; \(\alpha\)-admissible mapping

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References


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DOI: http://dx.doi.org/10.26713%2Fcma.v9i3.793

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