Meir–Keeler Type Contraction in Orthogonal M-Metric Spaces

Abstract

In this article, we prove fixed point results for a Meir–Keeler type contraction due to orthogonal M-metric spaces. The results of the paper improve and extend some recent developments in fixed point theory. The extension is assured by the concluding remarks and followed by the main theorem. Finally, an application of the main theorem is established in proving theorems for some integral equations and integral-type contractive conditions.

On Some Inequalities Involving Generalized Distance Functions

“…In many branches of mathematical analysis, having a metric structure is essential for the study of several problems. For instance, the concept of distance between elements of an abstract set allows us to define many topological properties, such as convergence, Cauchy sequences, continuity and others [1][2][3][4]. One of the important properties of a (standard) distance function D on an abstract set M is the triangle inequality, i.e., D(u, v) ≤ D(u, w) + D(w, v) for all u, v.w ∈ M.…”