# Generalizations of Caristi Kirk's Theorem on Partial Metric Spaces

@article{Karapnar2011GeneralizationsOC, title={Generalizations of Caristi Kirk's Theorem on Partial Metric Spaces}, author={Erdal Karapınar}, journal={Fixed Point Theory and Applications}, year={2011}, volume={2011}, pages={1-7} }

In this article, lower semi-continuous maps are used to generalize Cristi-Kirk's fixed point theorem on partial metric spaces. First, we prove such a type of fixed point theorem in compact partial metric spaces, and then generalize to complete partial metric spaces. Some more general results are also obtained in partial metric spaces.2000 Mathematics Subject Classification 47H10,54H25

## 166 Citations

### Generalizations of Caristi-Kirk theorem in partial metric spaces and applications

- Mathematics
- 2017

In this paper, some generalizations of Caristi-Kirk fixed point theorem in partial metric spaces are established, and applications of our results are given. Mathematics Subject Classification:47H10,…

### CARISTI'S TYPE MAPPINGS ON COMPLETE PARTIAL METRIC SPACES

- Mathematics
- 2013

We introduce a new type of Caristi's mapping on partial metric spaces and show that a partial metric space is complete if and only if every Caristi mapping has a fixed point. From this result we…

### FIXED POINT THEOREM FOR GENERALIZED SET-VALUED CONTRACTIONS ON PARTIAL METRIC SPACES

- Mathematics
- 2017

In this paper, a new version of Ekeland’s variational principle on partial metric spaces is given. Using this variational principle, we establish a general result on the existence of a fixed point…

### Some Common Fixed Point Theorems in Partial Metric Spaces

- MathematicsJ. Appl. Math.
- 2011

Some well-known results on common fixed point are investigated and generalized to the class of partial metric spaces in which self-distance of points need not to be zero but the property of symmetric and modified version of triangle inequality is satisfied.

### Fixed Point Theorems on Partial Metric Spaces Involving Rational Type Expressions with C-Class Functions

- Mathematics
- 2017

In this paper, we present some fixed point theorems for contraction of rational type by using a class of pairs of functions satisfying certain assumptions with C-class functions in a complete partial…

### Stability results for generalized contractions in partial metric spaces

- Mathematics
- 2012

In 1994, Mathews [7] introduced the notion of partial metric spaces as a part of his study of denotational semantics of data.ow networks and obtained a generalization of the Banach contraction…

### Integral Type F-Contractions in Partial Metric Spaces

- MathematicsJournal of Function Spaces
- 2019

Partial metric spaces were introduced as a generalization of usual metric spaces where the self-distance for any point need not be equal to zero. In this work, we defined generalized integral type…

### A NOTE ON COMMON FIXED POINT THEOREMS IN PARTIAL METRIC SPACES

- Mathematics
- 2011

In this manuscript, we consider the notion of generalized Sehgal contraction condi- tion in a partial metric space. For the pair of two self mappings .S;T/ which satisfies Sehgal contraction…

### A common fixed point theorem for cyclic operators on partial metric spaces

- Mathematics
- 2012

In this paper, we prove a common fixed point theorem for two self-mappings satisfying certain conditions over the class of partial metric spaces. In particular, the main theorem of this manuscript…

## 9 References

### On Banach fixed point theorems for partial metric spaces

- Mathematics
- 2005

In this paper we prove several generalizations of the Banach fixed point theorem for partial metric spaces (in the sense of O’Neill) given in, obtaining as a particular case of our results the Banach…

### Banach's Fixed Point Theorem for Partial Metric Spaces

- Mathematics
- 2004

Summary. - In 1994, S.G. Matthews introduced the notion of a partial metric space and obtained, among other results, a Banach contraction mapping for these spaces. Later on, S.J. O’Neill generalized…

### Fixed Point Theorems for Monotone Mappings on Partial Metric Spaces

- Mathematics
- 2010

Matthews (1994) introduced a new distance on a nonempty set , which is called partial metric. If is a partial metric space, then may not be zero for . In the present paper, we give some fixed point…

### Existence and uniqueness of a common fixed point on partial metric spaces

- MathematicsAppl. Math. Lett.
- 2011

### Partial Metric Topology

- Mathematics
- 1994

This paper presents a symmetric generalised metric for such topologies, an approach which sheds new light on how metric tools such as Banach's Theorem can be extended to non‐Hausdorff topologies.

### Fixed point theorems for mapping satisfying inwardness conditions

- Mathematics
- 1976

Let X be a normed linear space and let K be a convex subset of X. The inward set, IK(x), of x relative to K is defined as follows: IK(x) = {x + c(u x):c ; 1, u E K}. A mapping T:K X is said to be…

### Sur les prob ’ emes variationnels

- CR Acad Sci Paris
- 1972