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

Awais Asif, Muhammad Nazam, Muhammad Arshad and Sang Og Kim
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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

Mathematics, 2019, vol. 7, issue 7, 1-13

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.

Keywords: ?-metric; Reich-type F -contraction; Kannan-type F -contraction; dynamic programming (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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