Some notes on convex F-contraction in b-metric spaces

Abstract

In this paper, a generalized version of convex F-contractions in bmetric
spaces and the notion of nearly continuity, which is weaker than
continuity, are introduced. By using these definitions, the existence and
uniqueness of the fixed points for a self-mapping in the setting of b-metric
spaces are discussed. The results of this article improve the main results
and answer the open problems raised in [7].