Let F:X-*X be a multifunction on a partially ordered set (X, ¿). Suppose for each pair «iá*2 and for each yi<EF(xi) there is a yi&F{y¿) such that yièyiThen sufficient conditions are given such that multifunctions F satisfying the above condition will have a fixed point. These results generalize the Tarski Theorem on complete lattices, and they also generalize some results of S. Abian and A. B. ...

We study the existence and uniqueness of solutions for boundary value problems associated to differential equations of interval-valued functions, by using the derivative of Hukuhara and some fixed point theorems for weakly contractive mappings defined on partially ordered sets.

Existence and approximation of best proximity points is an interesting topic for which one can see [2, 3, 4, 6, 5] for more information. Another extension of Banach contraction principle was given by Nieto and Rodriguez-Lopez in partially ordered metric spaces [9]. They proved some fixed point theorems in partially ordered sets in order to show the existence and uniqueness for a first-order ord...

Super-relational fixed point property for ordered sets is formulated. It is weaker than the strengthened fixed point property and stronger than the product property. It is a long-standing problem whether every ordered set with the fixed point property has the product property. Several attempts have been made which solved the problem for some important classes of ordered sets. What is known may ...

This paper is concerned with mixed monotone mappings in partially ordered cone metric spaces. We establish several fixed point theorems, which generalize and complement some known results. Especially, even in a partially ordered metric space, our main results are generalizations of the fixed point theorems due to Bhaskar and Lakshmikantham [T. Grana Bhaskar, V. Lakshmikantham, Fixed point theor...

In this paper, we prove several coupled common fixed point theorems for nonlinear mappings in a partially ordered probabilistic metric space. An example is presented to illustrate the main result of this paper.

Fixed point calculus is about the solution of recursive equations de ̨ned by a monotonic endofunction on a partially ordered set. This tutorial presents the basic theory of ̨xed point calculus together with a number of applications of direct relevance to the construction of computer programs. The tutorial also presents the theory and application of Galois connections between partially ordered se...

*Correspondence: [email protected] 1Departamento de Análise Matemática, Estatística e Optimización, Facultade de Matemáticas, Universidade de Santiago de Compostela, Santiago de Compostela, 15782, Spain Full list of author information is available at the end of the article Abstract We present the random version in partially ordered metric spaces of the classical Banach contraction prin...

As an application of the dual equivalence between the category of L-spatialC-objects and the category of L-sober C-M-L-spaces, it is shown in this paper that for a fixed augmented partially ordered set A, there exists a dual equivalence between the category of A-spatial augmented partially ordered sets and the category of A-sober A-valued spaces. Then, with regard to this duality, for a fixed (...

*Correspondence: [email protected] 1Department of Mathematics, Atilim University, İncek, Ankara 06836, Turkey Full list of author information is available at the end of the article Abstract The purpose of this paper is to extend some recent coupled fixed point theorems in the context of partially ordered G-metric spaces in a virtually different and more natural way. MSC: 46N40; 47H10; 54H25;...