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

Authors

  • Azhar Hussain Department of Mathematics, University of Sargodha, Sargodha
  • Tanzeela Kanwal Department of Mathematics, University of Sargodha, Sargodha
  • Ahmed Al-Rawashdeh Department of Mathematical Sciences, UAE University, 15551, Al Ain

DOI:

https://doi.org/10.26713/cma.v9i3.793

Keywords:

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

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.

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Published

25-09-2018
CITATION

How to Cite

Hussain, A., Kanwal, T., & Al-Rawashdeh, A. (2018). Global Best Approximate Solutions for Set Valued Contraction in \(b\)-metric Spaces with Applications. Communications in Mathematics and Applications, 9(3), 293–313. https://doi.org/10.26713/cma.v9i3.793

Issue

Vol. 9 No. 3 (2018)

Section

Research Article

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