Fixed point theorems on an orthogonal metric space using Matkowski type contraction

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.