Some Fixed-Point Theorems in Proximity Spaces with Applications

Muhammad Qasim, Hind Alamri, Ishak Altun and Nawab Hussain
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Muhammad Qasim: Department of Mathematics, School of Natural Sciences, National University of Sciences and Technology (NUST), H-12, Islamabad 44000, Pakistan
Hind Alamri: Department of Mathematics, Collage of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia
Ishak Altun: Department of Mathematics, Faculty of Science and Arts, Kırıkkale University, Yahsihan, Kırıkkale 71450, Turkey
Nawab Hussain: Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

Mathematics, 2022, vol. 10, issue 10, 1-12

Abstract: Considering the ω -distance function defined by Kostić in proximity space, we prove the Matkowski and Boyd–Wong fixed-point theorems in proximity space using ω -distance, and provide some examples to explain the novelty of our work. Moreover, we characterize Edelstein-type fixed-point theorem in compact proximity space. Finally, we investigate an existence and uniqueness result for solution of a kind of second-order boundary value problem via obtained Matkowski-type fixed-point results under some suitable conditions.

Keywords: fixed point; proximity spaces; ? -contraction; ? -distance (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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