Global best approximate solutions for set-valued cyclic α-F-contractions

In this paper, we introduce the concepts of multivalued cyclic α-F contraction and triangular α-orbital admissible mappings. We use these concepts to find global best approximation solutions in a metric space with proximally complete property. We also provide some nontrivial examples to support our results. As an application, we obtain best proximity point results in partially ordered metric spaces and best proximity point theorems for single-valued mappings. We also prove fixed point results for multivalued and single-valued α-type F-contractions.