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F -Metric, F -Contraction and Common Fixed-Point Theorems with Applications

Author

Listed:
  • Awais Asif

    (Department of Math & Stats, International Islamic University, Islamabad 44000, Pakistan)

  • Muhammad Nazam

    (Department of Mathematics, Allama Iqbal Open University, Islamabad 44000, Pakistan)

  • Muhammad Arshad

    (Department of Math & Stats, International Islamic University, Islamabad 44000, Pakistan)

  • Sang Og Kim

    (School of Data Science, Hallym University, Chuncheon 24252, Korea)

Abstract

In this paper, we noticed that the existence of fixed points of F -contractions, in F -metric space, can be ensured without the third condition (F3) imposed on the Wardowski function F : ( 0 , ∞ ) → R . We obtain fixed points as well as common fixed-point results for Reich-type F -contractions for both single and set-valued mappings in F -metric spaces. To show the usability of our results, we present two examples. Also, an application to functional equations is presented. The application shows the role of fixed-point theorems in dynamic programming, which is widely used in computer programming and optimization. Our results extend and generalize the previous results in the existing literature.

Suggested Citation

  • Awais Asif & Muhammad Nazam & Muhammad Arshad & Sang Og Kim, 2019. "F -Metric, F -Contraction and Common Fixed-Point Theorems with Applications," Mathematics, MDPI, vol. 7(7), pages 1-13, June.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:7:p:586-:d:244561
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