A New Best Proximity Point Result with an Application to Nonlinear Fredholm Integral Equations

Hakan Sahin
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Hakan Sahin: Department of Mathematics, Faculty of Science and Arts, Amasya University, Amasya 05000, Turkey

Mathematics, 2022, vol. 10, issue 4, 1-14

Abstract: In the current paper, we first introduce a new class of contractions via a new notion called p -cyclic contraction mapping by combining the ideas of cyclic contraction mapping and p -contraction mapping. Then, we give a new definition of a cyclically 0-complete pair to weaken the completeness condition on the partial metric spaces. Following that, we prove some best proximity point results for p -cyclic contraction mappings on D ∪ E where D , E is a cyclically 0-complete pair in the setting of partial metric spaces. Hence, we generalize and unify famous and well-known results in the literature of metric fixed point theory. Additionally, we present some nontrivial examples to compare our results with earlier. Finally, we investigate the sufficient conditions for the existence of a solution to nonlinear Fredholm integral equations by the results in the paper.

Keywords: best proximity point; p -cyclic contractions; nonlinear Fredholm integral equations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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