Condition In Partial Metric Spaces Research Articles

Boyd and Wong Type Fixed Point Theorems in Partial Metric Spaces

Abstract In this paper, we present fixed point results for Boyd and Wong type [3] generalized contractive condition in partial metric spaces. In particular, we generalize the fixed point results due to Akkouchi [1] in complete partial metric spaces in which the continuity requirement for a mapping is relaxed to obtain the results. In addition to that we present a common fixed point theorem for a pair of maps. An illustrative example is also constructed to exhibit the results.

Toward a generalized contractive condition in partial metric spaces with the existence results of fixed points and best proximity points

The aim of this paper is to define the new type of mappings which is called a weak $$\psi $$ - $$\phi $$ -contraction mapping. Fixed point theorems for such mappings in partial metric spaces are established. Moreover, we present an example and numerical result for the main result. By providing this example, we show that our main result is a real generalization of the fixed point results of several mathematicians in the literature. As an application, we apply our results to prove the existence theorems of best proximity points for the non-self mappings.

Some results of common fixed point for four self-maps satisfying a new Ψ -contractive condition in partial metric spaces

Some results of common fixed point for four self-maps satisfying a new Ψ -contractive condition in partial metric spaces

A Suzuki type unique common fixed point theorem for two pairs of hybrid maps under a new condition in partial metric spaces

Abstract In this paper, we introduce a new condition namely: condition (W.C.C.) and utilize the same to prove a Suzuki type unique common fixed point theorem for two hybrid pairs of mappings in partial metric spaces employing the partial Hausdorff metric which generalizes several known results of the existing literature proved in metric and partial metric spaces.

Fixed points for four maps related to generalized weakly contractive condition in partial metric spaces

We prove a unique fixed point theorem for a function depending from four self maps satisfying (φ-ψ)-contractive condition in partial metric spaces. Presented results extend and generalize some existing fixed point results in the literature

Unique Common Fixed Point Theorems for Pairs of Hybrid Maps under a New Condition in Partial Metric Spaces

Abstract In this paper, we introduce a new condition namely, ‘condition (W.C.C)’ and obtain two unique common fixed point theorems for pairs of hybrid mappings on a partial Hausdorff metric space without using any continuity and commutativity of the mappings.

A Suzuki type unique common fixed point theorem for hybrid pairs of maps under a new condition in partial metric spaces

Abstract In this paper, we introduce a new condition namely, the (W.C.C) condition and give some Suzuki-type, unique, common fixed-point theorems for pairs of hybrid mappings in partial metric spaces using a partial Hausdorff metric. These results generalize and extend the several comparable results in this literature in metric and partial metric spaces.

A Unique Common Fixed Point Theorem of Meir-Keeler Type in a Partial Metric Space

In this paper, we obtain a unique common fixed point theorem for four self mappings satisfying Meir-Keeler type contractive condition in partial metric spaces, which is slightly different from the result of Aydi and Karapinar [5].

Fixed point theory of cyclical generalized contractive conditions in partial metric spaces

The purpose of this paper is to study fixed point theorems for a mapping satisfying the cyclical generalized contractive conditions in complete partial metric spaces. Our results generalize or improve many recent fixed point theorems in the literature.

Fixed point theorems via various cyclic contractive conditions in partial metric spaces

We present some fixed point results for mappings which satisfy Hardy-Rogers rational type, quasicontraction type, weak contraction type and generalized f? type cyclic conditions in 0-complete partial metric spaces. Presented results generalize or improve many existing fixed point theorems in the literature. To demonstrate our results, we give throughout the paper some examples. One of the possible applications of our results to well-posed and limit shadowing property of fixed point problems is also presented.

Multidimensional Fixed-Point Theorems in Partially Ordered Complete Partial Metric Spaces under ()-Contractivity Conditions

We study the existence and uniqueness of coincidence point for nonlinear mappings of any number of arguments under a weak ()-contractivity condition in partial metric spaces. The results we obtain generalize, extend, and unify several classical and very recent related results in the literature in metric spaces (see Aydi et al. (2011), Berinde and Borcut (2011), Gnana Bhaskar and Lakshmikantham (2006), Berzig and Samet (2012), Borcut and Berinde (2012), Choudhury et al. (2011), Karapınar and Luong (2012), Lakshmikantham and Ćirić (2009), Luong and Thuan (2011), and Roldán et al. (2012)) and in partial metric spaces (see Shatanawi et al. (2012)).

A unique common coupled fixed point theorem for four maps under Ψ-Φ contractive condition in partial metric spaces

In this paper, we obtain a unique coupled common fixed point theorem for four maps in partial metric spaces.

A unique common fixed-point theorem for two maps under ψ-ϕ contractive condition in partial metric spaces

PurposeThe purpose of this paper is to study a common fixed point theorem for two maps in partial metric spaces.MethodsTo prove Cauchy sequence, we used Ψ−Φ contractive method and obtain common fixed points.ResultsWe obtained a common fixed point result and illustrated with one example.ConclusionsIt is concluded from the present study that one can generalize some results from metric spaces to partial metric spaces.

Fixed point results under various contractive conditions in partial metric spaces

Some new fixed point and common fixed point results for mappings in partial metric spaces are obtained. Various conditions such as Hardy–Rogers-type, quasicontraction type and weak contractive type conditions are used. Moreover, properties (P) and (Q) are investigated. Examples are presented to show how these results can be used.