Abstract
After the establishment of the Banach contraction principle, the notion of metric space has been expanded to more concise and applicable versions. One of them is the conception ofℱ-metric, presented by Jleli and Samet. Following the work of Jleli and Samet, in this article, we establish common fixed points results of Reich-type contraction in the setting ofℱ-metric spaces. Also, it is proved that a unique common fixed point can be obtained if the contractive condition is restricted only to a subset closed ball of the wholeℱ-metric space. Furthermore, some important corollaries are extracted from the main results that describe fixed point results for a single mapping. The corollaries also discuss the iteration of fixed point for Kannan-type contraction in the closed ball as well as in the wholeℱ-metric space. To show the usability of our results, we present two examples in the paper. At last, we render application of our results.
Highlights
Introduction and PreliminariesIn recent years, along with F-metric presented by Jleli et al [1], many authors presented interesting generalizations of metric spaces [2,3,4,5,6,7,8,9]
Banach contraction principle states that any contraction on a complete metric space has a unique fixed point. is principle guarantees the existence and uniqueness of the solution of considerable problems arising in mathematics
Because of its importance for mathematical theory, the Banach contraction principle has been extended and generalized in many directions [10, 11]. e fixed point theory of multivalued contraction mappings using the Hausdorff metric was initiated by Nadler [12], who extended the Banach contraction principle to multivalued mappings
Summary
Introduction and PreliminariesIn recent years, along with F-metric presented by Jleli et al [1], many authors presented interesting generalizations of metric spaces [2,3,4,5,6,7,8,9]. Banach contraction principle states that any contraction on a complete metric space has a unique fixed point. Nazam et al [13] proved fixed point theorems for Kannan-type contractions on closed balls in complete partial metric spaces.
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