Let (X, d) a metric space and BX = X × R denote the partially ordered set of (generalized) formal balls in X. We investigate the topological structures of BX, in particular the relations between the Lawson topology and the product topology. We show that the Lawson topology coincides with the product topology if (X, d) is a totally bounded metric space, and show examples of spaces for which the ...

Let (X, d, ) be a partially ordered metric space. Let F, G be two set valued mappings and f , g two single valued mappings on X . We obtained sufficient conditions for existence of common fixed point of F , G, f and g satisfying an implicit relation in X .

Let (X, d,1) be a partially ordered metric space. Let F, G be two set valued mappings on X. We obtained sufficient conditions for the existence of a common fixed point of F , G satisfying an implicit relation in X. AMS subject classifications: 47H10, 47H04, 47H07

In this paper, we consider the concept of Ω-distance on a complete, partially ordered G-metric space and prove a fixed point theorem for (ψ, φ)-Weak contraction. Then, we present some applications in integral equations. c ©2013 All rights reserved.

In this paper, by reducing of coincidence and coupled fixed point results in ordered metric spaces to the respective results for mappings with one variable, some recent results established by T. G. Bhaskar and V. Lakshmikantham [T. G. Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Analysis 65 (2006) 1379-1393], V. Lakshmikantham a...

In 2014, Zead Mustafa introduced $b_2$-metric spaces, as a generalization of both $2$-metric and $b$-metric spaces. Then new fixed point results for the classes of  rational Geraghty contractive mappings of type I,II and III in the setup of $b_2$-metric spaces are investigated. Then, we prove some fixed point theorems under various contractive conditions in partially ordered $b_2$-metric spaces...