New fixed point theorems for orthogonal $F_m$-contractions in incomplete $m$-metric spaces

Abstract

In this paper, we introduce the concept of orthogonal $m$-metric spaces and by using $F_m$-contraction in orthogonal $m$-metric spaces, we give the concept of orthogonal $F_m$-contraction (briefly, $\bot_{F_m}$-contraction) and investigate fixed point results for such mappings. Many existing results in the literature appear to be special case of results proved in this paper. An example to support our main results is also mentioned.

Keywords

• unique fixed point
• orthogonal
• complete
• $\bot_{f_m}$-contraction
• incomplete $m$-metric space