scholarly journals Some best proximity point results for multivalued mappings on partial metric spaces

2021 ◽  
Vol 25 (1) ◽  
pp. 99-111
Author(s):  
Mustafa Aslantas ◽  
Al-Zuhairi Abed
Keyword(s):  
Contraction Mapping ◽  
Metric Spaces ◽  
Best Proximity Point ◽  
Multivalued Mappings ◽  
Partial Metric ◽  
Multivalued Contraction ◽  
New Concepts ◽  
Partial Metric Spaces

In this paper, we introduce two new concepts of Feng-Liu type multivalued contraction mapping and cyclic Feng-Liu type multivalued contraction mapping. Then, we obtain some new best proximity point results for such mappings on partial metric spaces by considering Feng-Liu's technique. Finally, we provide examples to show the effectiveness of our results.

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 A Suzuki-type multivalued contraction on weak partial metric spaces and applications

2018 ◽  
Vol 2018 (1) ◽  
Author(s):  
Hassen Aydi ◽  
M. A. Barakat ◽  
Zoran D. Mitrović ◽  
Vesna Šešum-Čavić
Keyword(s):  
Metric Spaces ◽  
Partial Metric ◽  
Multivalued Contraction ◽  
Partial Metric Spaces

scholarly journals Best Proximity Results on Dualistic Partial Metric Spaces

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 306 ◽  
Author(s):  
Ariana Pitea
Keyword(s):  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Best Proximity Point ◽  
Auxiliary Function ◽  
Partial Metric ◽  
Partial Metric Spaces

We introduce the generalized almost ( φ , θ ) -contractions by means of comparison type functions and another kind of mappings endowed with specific properties in the setting of dualistic partial metric spaces. Also, generalized almost θ -Geraghty contractions in the setting of dualistic partial metric spaces are defined by the use of a function of Geraghty type and another adequate auxiliary function. For these classes of generalized contractions, we have stated and proved the existence and uniqueness of a best proximity point.

scholarly journals Common Best Proximity Point Results for T-GKT Cyclic ϕ-Contraction Mappings in Partial Metric Spaces with Some Applications

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1098
Author(s):  
Nilakshi Goswami ◽  
Raju Roy ◽  
Vishnu Narayan Mishra ◽  
Luis Manuel Sánchez Ruiz
Keyword(s):  
Integral Equation ◽  
Metric Spaces ◽  
Best Proximity Point ◽  
Partial Metric ◽  
Existence Of A Solution ◽  
Contraction Mappings ◽  
Common Best Proximity Point ◽  
New Class ◽  
Partial Metric Spaces

The aim of this paper is to derive some common best proximity point results in partial metric spaces defining a new class of symmetric mappings, which is a generalization of cyclic ϕ-contraction mappings. With the help of these symmetric mappings, the characterization of completeness of metric spaces given by Cobzas (2016) is extended here for partial metric spaces. The existence of a solution to the Fredholm integral equation is also obtained here via a fixed-point formulation for such mappings.

scholarly journals Best Approximation Results in Various Frameworks

Axioms ◽  
2019 ◽  
Vol 8 (2) ◽  
pp. 67
Author(s):  
Taoufik Sabar ◽  
Abdelhafid Bassou ◽  
Mohamed Aamri
Keyword(s):  
Best Approximation ◽  
Metric Spaces ◽  
Best Proximity Point ◽  
Nonexpansive Mappings ◽  
Partial Metric ◽  
Relatively Nonexpansive Mappings ◽  
Partial Metric Spaces ◽  
Relatively Nonexpansive ◽  
Cyclic Mapping

We first provide a best proximity point result for quasi-noncyclic relatively nonexpansive mappings in the setting of dualistic partial metric spaces. Then, those spaces will be endowed with convexity and a result for a cyclic mapping will be obtained. Afterwards, we prove a best proximity point result for tricyclic mappings in the framework of the newly introduced extended partial S b -metric spaces. In this way, we obtain extensions of some results in the literature.

scholarly journals Some New Fixed Point Theorems in Partial Metric Spaces with Applications

2017 ◽  
Vol 2017 ◽  
pp. 1-13 ◽  
Author(s):  
Rajendra Pant ◽  
Rahul Shukla ◽  
H. K. Nashine ◽  
R. Panicker
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Type System ◽  
Multivalued Mappings ◽  
Partial Metric ◽  
Volterra Type ◽  
System Of Integral Equations ◽  
Partial Metric Spaces ◽  
Contraction Type

Recently, a number of fixed point theorems for contraction type mappings in partial metric spaces have been obtained by various authors. Most of these theorems can be obtained from the corresponding results in metric spaces. The purpose of this paper is to present certain fixed point results for single and multivalued mappings in partial metric spaces which cannot be obtained from the corresponding results in metric spaces. Besides discussing some useful examples, an application to Volterra type system of integral equations is also discussed.

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.

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