A new type of \(F\)-contraction and their best proximity point results with homotopy application. (English) Zbl 1498.54100
The author extends and unifies previous results for multivalued \(F\)-contractions, in a different way from the results in the literature without using the Pompeiu-Hausdorff metric. However, the author has firstly introduced a new class of multivalued mappings that includes multivalued \(F\)-contractions. Some best proximity point results for new kinds of \(F\)-contraction mappings are derived. Some nontrivial and interesting examples are given in order to unify and improve many results in the literature. Also, the author has applied the main result of the article to homotopy theory.
Reviewer: Memudu Olaposi Olatinwo (Ile-Ife)
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