Abstract

The aim of this paper is to present some new observations about $w$-distance (in the sense of O. Kada, T. Suzuki, W. Takahashi, \emph{Nonconvex minimization theorems and fixed point theorems in complete metric spaces}, Math.\ Japonica \textbf{44}, 2 (1996), 381--391) and $F$-contractions (in the sense of D. Wardowski, \emph{Fixed points of a new type of contractive mappings in complete metric spaces}, Fixed Point Theory Appl., \textbf{2012}:94 (2012)). Both concepts have been examined separately a lot, but there have been few attempts to connect them. This article is a step in filling this gap. Besides, some comments and improvements of results in the existing literature are presented.

Keywords: $w$-distance; $wt$-distance; $F$-contraction; $b$-metric space; metric-like space.

MSC: 47H10, 54H25

DOI: 10.57016/MV-UxZA2735

Pages:  43$-$55     

Volume  76 ,  Issue  1-2 ,  2024