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 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...

Suppose X is a partially ordered real Banach space such that there is a 2−norm on X. The purpose of this paper is to prove coupled coincidence and coupled common fixed point theorems for mappings from X ×X to X.

The U(1) Calogero Sutherland Model (CSM) with anti-periodic boundary condition is studied. The Hamiltonian is reduced to a convenient form by similarity transformation. The matrix representation of the Hamiltonian acting on a partially ordered state space is obtained in an upper triangular form. Consequently the diagonal elements become the energy eigenvalues.

Hierarchical structures and uncertainty measures are two main aspects in granular computing, approximate reasoning and cognitive process. Typical hesitant fuzzy sets, as a prime extension of fuzzy sets, are more flexible to reflect the hesitance and ambiguity in knowledge representation and decision making. In this paper, we mainly investigate the hierarchical structures and uncertainty measure...

poverty can have spatial dimensions. while general figures might show the spatial pattern of poverty, there is a need for more detailed examination of this pattern. relying on simple figures of spatial patterns and ranking regions based on them might be misleading. this paper tries to apply spatial analysis methodsm, namely spatial autoregressive models to find out the impacts of space on the h...