Fixed point results via a Hausdorff controlled type metric

Abstract

In this paper, we establish that every controlled metric space (X, dα) induces a Hausdorff controlled metric (Hα, CLD(X)) on the class of closed subsets of X which is also complete if (X, dα) is complete. Furthermore, we define multivalued almost F-contractions on Hausdorff controlled metric spaces and prove some fixed point results.