in this note we point out and rectify some errors in a recently published paper “n. singh, r. jain: coupled fixed point results for weakly related mappings in partially ordered metric spaces, bull. iranian math. soc. 40 (2014), no. 1, 29-40”.

in the present paper‎, ‎we show the existence of a coupled fixed point for a non-decreasing mapping in partially ordered complete metric space using a partial order induced by an appropriate function $phi$‎. ‎we also define the concept of weakly related mappings on an ordered space‎. ‎moreover common coupled fixed points for two and three weakly related mappings are also proved in the same space‎.

in this paper we define weak $f$-contractions on a‎ ‎metric space into itself by extending $f$-contractions‎ ‎introduced by d‎. ‎wardowski (2012) and provide some fixed point‎ ‎results in complete metric spaces and in partially ordered complete ‎generalized metric spaces‎. ‎some relationships between weak‎ ‎$f$-contractions and $fi$-contractions are highlighted‎. ‎we also ‎give some application...

This set of notes is prepared for the Meander Group (MG) at Brigham Young University. Its purpose is to introduce MG to: (1) the basic definitions and theorems of partially ordered set theory and (2) the various combinatorial methods associated with partially ordered sets.

We consider the concept of Ω-distance on a complete partially ordered G-metric space and prove some common fixed point theorems.

Given an abelian length category A, the Gabriel-Roiter measure with respect to a length function l is characterized as a universal morphism indA → P of partially ordered sets. The map is defined on the isomorphism classes of indecomposable objects of A and is a suitable refinement of the length function l. In his proof of the first Brauer-Thrall conjecture [5], Roiter used an induction scheme w...

A pair of linear orders L, L′ on an n-element set V is a concordance pair if the Kendall and Spearman correlation measures between L and L′ coincide. A graph is called concordance graph if it has the same number of induced three-vertex one-edged subgraphs as induced three-vertex twoedged subgraphs. It is known (see Fishburn and Monjardet (2000)) that (L, L′) is a concordance pair if and only if...

Given a mapping f : A → B from a partially ordered set A into an unstructured set B, we study the problem of defining a suitable partial ordering relation on B such that there exists a mapping g : B → A such that the pair of mappings (f, g) forms an isotone Galois connection between partially ordered sets.

In this paper we will show that partially ordered monads contain sufficient structure for modelling monadic topologies, rough sets and Kleene algebras. Convergence represented by extension structures over partially ordered monads includes notions of regularity and compactness. A compactification theory can be developed. Rough sets [23] are modelled in a generalized setting with set functors. Fu...

Lcclerc proved that the dimension of the partiailly ordered slet consisting of all subf~ce'~ of a tree T, m&red by inclusion, is the number of end yuints of 'I'. Leclerc posed the probkrn of determitAng the dimension the partially ed set P consisting of all inducxxI connected subgraphs of a connec graph G for tPisa lattice. In this paper, WC prove that the poset P consisting af all induced conn...