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Some Fixed-Point Theorems in Proximity Spaces with Applications

Author

Listed:
  • 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)

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.

Suggested Citation

  • Muhammad Qasim & Hind Alamri & Ishak Altun & Nawab Hussain, 2022. "Some Fixed-Point Theorems in Proximity Spaces with Applications," Mathematics, MDPI, vol. 10(10), pages 1-12, May.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:10:p:1724-:d:818313
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