Search results for "Ordered metric space"
showing 8 items of 8 documents
Fixed point theorems on ordered metric spaces and applications to nonlinear elastic beam equations
2012
In this paper, we establish certain fixed point theorems in metric spaces with a partial ordering. Presented theorems extend and generalize several existing results in the literature. As application, we use the fixed point theorems obtained in this paper to study existence and uniqueness of solutions for fourth-order two-point boundary value problems for elastic beam equations.
Fixed Point Theorems in Partially Ordered Metric Spaces and Existence Results for Integral Equations
2012
We derive some new coincidence and common fixed point theorems for self-mappings satisfying a generalized contractive condition in partially ordered metric spaces. As applications of the presented theorems, we obtain fixed point results for generalized contraction of integral type and we prove an existence theorem for solutions of a system of integral equations.
Fixed point results for F-contractive mappings of Hardy-Rogers-type
2014
Recently, Wardowski introduced a new concept of contraction and proved a fixed point theorem which generalizes Banach contraction principle. Following this direction of research, in this paper, we will present some fixed point results of Hardy-Rogers-type for self-mappings on complete metric spaces or complete ordered metric spaces. Moreover, an example is given to illustrate the usability of the obtained results.
Suzukiʼs type characterizations of completeness for partial metric spaces and fixed points for partially ordered metric spaces
2012
Abstract Recently, Suzuki [T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc. Amer. Math. Soc. 136 (2008) 1861–1869] proved a fixed point theorem that is a generalization of the Banach contraction principle and characterizes the metric completeness. In this paper we prove an analogous fixed point result for a self-mapping on a partial metric space or on a partially ordered metric space. Our results on partially ordered metric spaces generalize and extend some recent results of Ran and Reurings [A.C.M. Ran, M.C. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc. 132 (2004…
Multi-valued F-contractions and the solution of certain functional and integral equations
2013
Wardowski [Fixed Point Theory Appl., 2012:94] introduced a new concept of contraction and proved a fixed point theorem which generalizes Banach contraction principle. Following this direction of research, we will present some fixed point results for closed multi-valued F-contractions or multi-valued mappings which satisfy an F-contractive condition of Hardy-Rogers-type, in the setting of complete metric spaces or complete ordered metric spaces. An example and two applications, for the solution of certain functional and integral equations, are given to illustrate the usability of the obtained results.
Graphical metric space: a generalized setting in fixed point theory
2016
Building on recent ideas of Jachymski, we work on the notion of graphical metric space and prove an analogous result for the contraction mapping principle. In particular, the triangular inequality is replaced by a weaker one, which is satisfied by only those points which are situated on some path included in the graphical structure associated with the space. Some consequences, examples and an application to integral equations are presented to confirm the significance and unifying power of obtained generalizations.
Fixed point theorems for twisted (α,β)-ψ-contractive type mappings and applications
2013
The purpose of this paper is to discuss the existence and uniqueness of fixed points for new classes of mappings defined on a complete metric space. The obtained results generalize some recent theorems in the literature. Several applications and interesting consequences of our theorems are also given.
Coupled coincidence point results for (φ,ψ)-contractive mappings in partially ordered metric spaces
2014
Abstract. In this paper, we extend the coupled coincidence point theorems for a mixed g-monotone operator F : X × X → X $F:X\times X\rightarrow X$ obtained by Alotaibi and Alsulami [Fixed Point Theory Appl. (2011), article ID 44], by weakening the involved contractive condition. Two examples are given to illustrate the effectiveness of our generalizations. Our result also generalizes some recent results announced in the literature. Moreover, some applications to integral equations are presented.