The main purpose of this research is to extend some fixed point results in orthogonal metric spaces. For this purpose, first, we investigate new mappings in this spaces. We introduce the new notions of functions. Then by using it, we define contractive mappings and then we establish and prove some fixed point theorems for such mappings in orthogonal metric spaces. Then by utilizing examples of ...

in this paper, we introduce a concept of a generalized $c$-distance in ordered cone $b$-metric spaces and, by using the concept, we prove some fixed point theorems in ordered cone $b$-metric spaces. our results generalize the corresponding results obtained by y. j. cho, r. saadati, shenghua wang (y. j. cho, r. saadati, shenghua wang, common fixed point  heorems on generalized distance in ordere...

In this paper, we improve some recent coupled fixed point resultsfor single-valued operators in the framework of ordered $b$-metricspaces established by Bota et al. [M-F. Bota, A. Petrusel, G.Petrusel and B. Samet, Coupled fixed point theorems forsingle-valued operators in b-metric spaces, Fixed Point TheoryAppl. (2015) 2015:231]. Also, we prove that Perov-type fix...

In this paper, we introduce tripled partially ordered sets and monotone functions on tripled partiallyordered sets. Some basic properties on these new dened sets are studied and some examples forclarifying are given.

Partially ordered sets and metric spaces are used in studying semantics in Computer Science. Sets with both these structures are hence of particular interest. The partial metric spaces introduced by Matthews are an attempt to bring these ideas together in a single axiomatic framework. We consider an appropriate context in which to consider these spaces is as a bitopo-logical space, i.e. a space...

*Correspondence: [email protected] 1Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia Full list of author information is available at the end of the article Abstract The notion of modular metric space, being a natural generalization of classical modulars over linear spaces, was recently introduced. In this paper, we introduce a generalized F-contr...