Setting Of Partial Metric Spaces Research Articles

Proximity Point Results for Generalized p-Cyclic Reich Contractions: An Application to Solving Integral Equations

This article studies new classes of contractions called the p-cyclic Reich contraction and p-cyclic Reich contraction pair and develops certain best proximity point results for such contractions in the setting of partial metric spaces. Furthermore, the best proximity point results for p-proximal cyclic Reich contractions of the first and second types are also discussed.

A New Best Proximity Point Result with an Application to Nonlinear Fredholm Integral Equations

In the current paper, we first introduce a new class of contractions via a new notion called p-cyclic contraction mapping by combining the ideas of cyclic contraction mapping and p-contraction mapping. Then, we give a new definition of a cyclically 0-complete pair to weaken the completeness condition on the partial metric spaces. Following that, we prove some best proximity point results for p-cyclic contraction mappings on D∪E where D,E is a cyclically 0-complete pair in the setting of partial metric spaces. Hence, we generalize and unify famous and well-known results in the literature of metric fixed point theory. Additionally, we present some nontrivial examples to compare our results with earlier. Finally, we investigate the sufficient conditions for the existence of a solution to nonlinear Fredholm integral equations by the results in the paper.

Almost $alpha$-$F$-contraction, fixed points and applications

In this manuscript, we initiate an almost $alpha$-$F$-contraction and an almost $alpha$-$F$- weak contraction in the setting of partial metric spaces and establish adequate conditions for the presence of fixed points. The obtained results generalize the classical and recent results of the literature, which are validated by suitable examples. As applications of these established results, we solve a nonlinear fractional differential equation and a boundary value problem.

A local fixed point theorem for set-valued mappings on partial metric spaces

The purpose of this paper is to study the existence and location of fixed points for pseudo-contractive-type set-valued mappings in the setting of partial metric spaces by using Bianchini-Grundolfi gauge functions.

Iterative approximation of fixed points of Prešić operators on partial metric spaces

We study the convergence of the Prešić type k‐step iterative method for a class of operators satisfying Prešić type contractive conditions on the setting of partial metric spaces. Some examples are presented to illustrate our obtained results. As applications of the presented convergence theorems, we derive global attractivity results for a class of matrix difference equations. Numerical experiments are also presented to illustrate the theoretical findings.

Fixed points for Geraghty-Contractions in partial metric spaces

We establish some fixed point theorems for mappings satisfying Geraghty-type contractive conditions in the setting of partial metric spaces and ordered partial metric spaces. Presented theorems extend and generalize many existing results in the literature. Examples are given showing that these results are proper extensions of the existing ones. c ©2014 All rights reserved.

Common fixed points for generalized $$\alpha $$ α -implicit contractions in partial metric spaces: consequences and application

In this paper, we introduce the concept of generalized \(\alpha \)-admissible pair of mappings generalizing the definition of \(\alpha \)-admissible mappings presented by Samet et al. (Nonlinear Anal 75:2154–2165, 2012). Based on above, we define generalized \(\alpha \)-implicit contractions in the setting of partial metric spaces and we provide some common fixed point results for such contractions. We also derive some consequences and corollaries from our obtained results. An application and some examples are presented making effective the new concepts and results.

Metric or partial metric spaces endowed with a finite number of graphs: A tool to obtain fixed point results

We give some fixed point theorems in the setting of metric spaces or partial metric spaces endowed with a finite number of graphs. The presented results extend and improve several well-known results in the literature. In particular, we discuss a Caristi type fixed point theorem in the setting of partial metric spaces, which has a close relation to Ekelandʼs principle.

Common fixed points of mappings satisfying implicit relations in partial metric spaces

Matthews, [S. G. Matthews, Partial metric topology, in: Proc. 8th Summer Conference on General Topology and Applications, in: Ann. New York Acad. Sci., vol. 728, 1994, pp. 183-197], introduced and studied the concept of partial metric space, as a part of the study of denotational semantics of data flow networks. He also obtained a Banach type fixed point theorem on complete partial metric spaces. Very recently Berinde and Vetro, [V. Berinde, F. Vetro, Common fixed points of mappings satisfying implicit contractive conditions, Fixed Point Theory and Applications 2012, 2012:105], discussed, in the setting of metric and ordered metric spaces, coincidence point and common fixed point theorems for self-mappings in a general class of contractions defined by an implicit relation. In this work, in the setting of partial metric spaces, we study coincidence point and common fixed point theorems for two self-mappings satisfying generalized contractive conditions, defined by implicit relations. Our results unify, extend and generalize some related common fixed point theorems of the literature.

Tripled coincidence and fixed point results in partial metric spaces

In this paper, we introduce the concept of W-compatiblity of mappings F : X × X × X ! X and g : X ! X and based on this notion, we obtain tripled coincidence and common tripled fixed point results in the setting of partial metric spaces. The presented results generalize and extend several well known comparable results in the existing literature. We also provide an example to support our results.

From metric spaces to partial metric spaces

Motivated by experience from computer science, Matthews (1994) introduced a nonzero self-distance called a partial metric. He also extended the Banach contraction principle to the setting of partial metric spaces. In this paper, we show that fixed point theorems on partial metric spaces (including the Matthews fixed point theorem) can be deduced from fixed point theorems on metric spaces. New fixed point theorems on metric spaces are established and analogous results on partial metric spaces are deduced. MSC:47H10, 54H25.

Fixed Points for Weakα-ψ-Contractions in Partial Metric Spaces

Recently, Samet et al. (2012) introduced the notion ofα-ψ-contractive mappings and established some fixed point results in the setting of complete metric spaces. In this paper, we introduce the notion of weakα-ψ-contractive mappings and give fixed point results for this class of mappings in the setting of partial metric spaces. Also, we deduce fixed point results in ordered partial metric spaces. Our results extend and generalize the results of Samet et al.

A Fixed Point Theorem for Multifunctions in Partial Metric spaces

Fixed Point theorems on partial metric spaces have been the subject of recent work, with the interest generated in partial metric spaces (as a suitable structure for studies in theoretical computer science). Several approaches to fixed point theory for point-valued functions on complete metric spaces have been generalized to partial metric spaces (see, for instance, Alghamdi [1]). On the other hand, it appears that substantial work may still be done to generalize the theory (in the partial metric space context) to set-valued functions. Recently, Damjanovic et al [3] looked into pairs of multi-valued and single-valued maps in complete metric spaces, and used coincidence and common fixed points, to establish a theorem on fixed points for pairs of multivalued functions. In this paper we take off from Damjanovic and proceed to establish the same result in the setting of partial metric spaces. As a consequence of our generalization, we are able to include as special cases the theorem of Aydi et al [2] and our [9] generalization of [4]. Further, Reich's result is also generalized to multivalued functions in partial metric spaces. Special cases include the partial metric space version of Kannan's theorem, as well as that due to Hardy and Rogers.

Fixed point theorems for expanding mappings in partial metric spaces

AbstractIn this paper, we define expanding mappings in the setting of partial metric spaces analogous to expanding mappings in metric spaces. We also obtain some results for two mappings to the setting of partial metric spaces

Generalization of Some Coupled Fixed Point Results on Partial Metric Spaces

Using the setting of partial metric spaces, we prove some coupled fixed point results. Our results generalize several well-known comparable results of H. Aydi (2011). Also, we introduce an example to support our results.