No 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.

The purpose of this paper is to prove Boyd-Wong and Matkowski type fixed point theorems in orthogonal metric space which was defined by M.E. Gordji in 2017 and is an extension of the metric space. Some examples are established in support of our main results. Finally, we apply our results to establish the existence of a unique solution of a periodic boundary value problem.

Recently, in 2021, Bijender et al. proposed the establishment of  -contraction. Such sort of contraction is a genuine generalization of the standard contraction in the study of metric fixed point theory. The aim of the present study is the establishment of the novel concept of the fuzzy B-type contraction in the settings of fuzzy metric space and such contractions are also used to establish a few fixed point theorems.