Orthogonal metric space and convex contractions

Document Type : Research Paper


Faculty of Mathematics, University of Bojnord, Bojnord, Iran


‎In this paper, generalized convex contractions on orthogonal metric spaces are stablished in whath  might be called their  definitive versions. Also, we show that there are examples which show that our main theorems are  genuine generalizations of Theorem 3.1 and 3.2 of [M.A. Miandaragh, M. Postolache and S. Rezapour,  {\it Approximate fixed points of generalized convex contractions}, Fixed Point Theory and Applications 2013,  2013:255].