scholarly journals Fixed Point Theory for Cyclic Generalized Weak -Contraction on Partial Metric Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Erdal Karapınar ◽  
I. Savas Yuce
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Partial Metric Space ◽  
Point Theory ◽  
Partial Metric ◽  
Weak Contraction ◽  
Partial Metric Spaces ◽  
Generalized Weak Contraction

A new fixed point theorem is obtained for the class of cyclic weak -contractions on partially metric spaces. It is proved that a self-mapping on a complete partial metric space has a fixed point if it satisfies the cyclic weak -contraction principle.

scholarly journals Existence of Fixed Point Under Generalized Multivalued - -Contraction in Partial Metric Spaces

2021 ◽  
Vol 16 (1) ◽  
Author(s):  
Smita Negi ◽  
Umesh Chandra Gairola
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Contraction Mapping ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Partial Metric Space ◽  
Point Theory ◽  
Partial Metric ◽  
Multivalued Contraction ◽  
Partial Metric Spaces

In this paper, we introduce the notion of generalized multivalued - -contraction in partial metric space endowed with an arbitrary binary relation and establish a fixed point theorem for this contraction mapping. Our result extends and generalize the result of Wardowski (Fixed Point Theory Appl. 2012:94 (2012)), Alam and Imdad (J. Fixed Point Theory Appl. 17 (4) (2015), 693–702) and Altun et al. (J. Nonlinear Convex Anal. 28 (16) (2015), 659-666). Also, we give an example to validate our result.

scholarly journals Fixed point results for Ciric typeweak contraction in metric spaces with applications to partial metric spaces

Filomat ◽  
2014 ◽  
Vol 28 (7) ◽  
pp. 1505-1516 ◽  
Author(s):  
Binayak Choudhury ◽  
A. Kundu ◽  
N. Metiya
Keyword(s):  
Fixed Point ◽  
Contraction Mapping ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Complete Metric Space ◽  
Point Theory ◽  
Partial Metric ◽  
Weak Contraction ◽  
Control Functions ◽  
Partial Metric Spaces

Partial metric spaces are generalizations of metric spaces which allow for non-zero self-distances. The need for such a definition was felt in the domain of computer science. Fixed point theory has rapidly developed on this space in recent times. Here we define a Ciric type weak contraction mapping with the help of discontinuous control functions and show that in a complete metric space such a function has a fixed point. Our main result has several corollaries and is supported with examples. One of the examples shows that the corollaries are properly contained in the theorem. We give applications of our results in partial metric spaces.

scholarly journals Some New Results on F-Contractions in 0-Complete Partial Metric Spaces and 0-Complete Metric-Like Spaces

2021 ◽  
Vol 5 (2) ◽  
pp. 34
Author(s):  
Stojan Radenović ◽  
Nikola Mirkov ◽  
Ljiljana R. Paunović
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Partial Metric Space ◽  
Point Theory ◽  
Partial Metric ◽  
Partial Metric Spaces ◽  
Fractional Differential ◽  
Theoretical Results

Within this manuscript we generalize the two recently obtained results of O. Popescu and G. Stan, regarding the F-contractions in complete, ordinary metric space to 0-complete partial metric space and 0-complete metric-like space. As Popescu and Stan we use less conditions than D. Wardovski did in his paper from 2012, and we introduce, with the help of one of our lemmas, a new method of proving the results in fixed point theory. Requiring that the function F only be strictly increasing, we obtain for consequence new families of contractive conditions that cannot be found in the existing literature. Note that our results generalize and complement many well-known results in the fixed point theory. Also, at the end of the paper, we have stated an application of our theoretical results for solving fractional differential equations.

scholarly journals FIXED POINTS FOR TWO PAIRS OF ABSORBING MAPPINGS IN WEAK PARTIAL METRIC SPACES

2020 ◽  
pp. 283
Author(s):  
Valeriu Popa ◽  
Alina-Mihaela Patriciu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Point Theorem ◽  
Metric Space ◽  
Metric Spaces ◽  
Partial Metric Space ◽  
Partial Metric ◽  
Partial Metric Spaces

In this paper, a general fixed point theorem for two pairs of absorbing mappings in weak partial metric space, using implicit relations, has been proved.

Fixed point results for mappings satisfying (ψ φ)-weakly contractive condition in ordered partial metric spaces

2013 ◽  
Vol 63 (4) ◽  
Author(s):  
Hemant Nashine
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Contractive Condition ◽  
Partial Metric ◽  
New Class ◽  
Weakly Contractive Condition ◽  
Partial Metric Spaces ◽  
Weakly Contractive

AbstractIn [18], Matthews introduced a new class of metric spaces, that is, the concept of partial metric spaces, or equivalently, weightable quasi-metrics, are investigated to generalize metric spaces (X, d), to develop and to introduce a new fixed point theory. In partial metric spaces, the self-distance for any point need not be equal to zero. In this paper, we study some results for single map satisfying (ψ,φ)-weakly contractive condition in partial metric spaces endowed with partial order. An example is given to support the useability of our results.

scholarly journals Conversions between generalized metric spaces and standard metric spaces with applications in fixed point theory

2021 ◽  
Vol 37 (2) ◽  
pp. 345-354
Author(s):  
ALEXANDRU-DARIUS FILIP
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Partial Metric ◽  
Generalized Metric Spaces ◽  
Generalized Metric ◽  
Partial Metric Spaces

In this paper we discuss similar problems posed by I. A. Rus in Fixed point theory in partial metric spaces (Analele Univ. de Vest Timişoara, Mat.-Inform., 46 (2008), 149–160) and in Kasahara spaces (Sci. Math. Jpn., 72 (2010), No. 1, 101–110). We start our considerations with an overview of generalized metric spaces with \mathbb{R}_+-valued distance and of generalized contractions on such spaces. After that we give some examples of conversions between generalized metric spaces and standard metric spaces with applications in fixed point theory. Some possible applications to theoretical informatics are also considered.

scholarly journals Some Fixed Point Theory Results for the Interpolative Berinde Weak Operator

2020 ◽  
pp. 253-271 ◽  
Author(s):  
Clement Boateng Ampadu
Keyword(s):  
Metric Spaces ◽  
Fixed Point Theory ◽  
Existence Theorems ◽  
Point Theory ◽  
Picard Iteration ◽  
Partial Metric ◽  
Weak Contraction ◽  
Nonlinear Anal ◽  
Partial Metric Spaces ◽  
Weak Operator

Partially inspired by [Erdal Karapinar, Ravi Agarwal and Hassen Aydi, Interpolative Reich-Rus-Ćirić type contractions on partial metric spaces, Mathematics 6 (2018), 256] and [V. Berinde, Approximating fixed points of weak contractions using the Picard iteration, Nonlinear Anal. Forum 9(1) (2004), 43-53], we introduce a concept of interpolative Berinde weak contraction, and obtain some existence theorems for mappings satisfying such a contractive definition, and some of its extensions.

scholarly journals Common fixed point results for generalized (ψ,β)-geraghty contraction type mapping in partially ordered metric-like spaces with application

Filomat ◽  
2017 ◽  
Vol 31 (17) ◽  
pp. 5497-5509 ◽  
Author(s):  
Habes Alsamir ◽  
Mohd Noorani ◽  
Wasfi Shatanawi ◽  
Kamal Abodyah
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Common Fixed Points ◽  
Partial Metric ◽  
Partially Ordered ◽  
Partial Metric Spaces ◽  
Contraction Type

Harandi [A. A. Harandi, Metric-like spaces, partial metric spaces and fixed points, Fixed Point Theory Appl., 2012 (2012), 10 pages] introduced the notion of metric-like spaces as a generalization of partial metric spaces and studied some fixed point theorems in the context of the metric-like spaces. In this paper, we utilize the notion of the metric-like spaces to introduce and prove some common fixed points theorems for mappings satisfying nonlinear contractive conditions in partially ordered metric-like spaces. Also, we introduce an example and an application to support our work. Our results extend and modify some recent results in the literature.

scholarly journals Some generalizations of Caristi type fixed point theorem on partial metric spaces

Filomat ◽  
2012 ◽  
Vol 26 (4) ◽  
pp. 833-837 ◽  
Author(s):  
Özlem Acar ◽  
Ishak Altun
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Metric Spaces ◽  
Partial Metric Space ◽  
Partial Metric ◽  
Partial Metric Spaces

In the persent paper, we give Bae and Suzuki type generalizations of Caristi?s fixed point theorem on partial metric space.

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