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.
Highlights
IntroductionMany authors have presented interesting generalizations of metric spaces (see for example [1,2,3,4,5,6,7,8,9,10,11])
In recent years, many authors have presented interesting generalizations of metric spaces
The application shows the role of fixed-point theorems in dynamic programming, which is widely used in computer programming and optimization
Summary
Many authors have presented interesting generalizations of metric spaces (see for example [1,2,3,4,5,6,7,8,9,10,11]). With the help of concrete examples, they obtained a similar result for s-relaxed metric space They discussed a relation between b-metric and F -metric spaces, defined a natural topology on these spaces and proved that after imposing a sufficient condition, the closed ball is closed with respect to the given topology. We relax the restrictions on Wardowski’s mapping [13] by eliminating the third condition and prove common fixed-point results of Reich-type F-contractions for both single and set-valued mappings in F -metric spaces.
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