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 Some Common Fixed Point Theorems forF-Contraction Type Mappings in 0-Complete Partial Metric Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Satish Shukla ◽  
Stojan Radenović
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Partial Metric ◽  
Partial Metric Spaces ◽  
Contraction Type ◽  
Common Fixed Point Theorems

We prove some common fixed point theorems forF-contractions in 0-complete partial metric spaces. Our results extend, generalize, and unify several known results in the literature. Some examples are included which show that the generalization is proper.

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

2013 ◽  
Vol 93 (107) ◽  
pp. 69-93 ◽  
Author(s):  
Hemant Nashine ◽  
Zoran Kadelburg ◽  
Stojan Radenovic
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Partial Metric ◽  
Shadowing Property ◽  
Partial Metric Spaces ◽  
Limit Shadowing ◽  
Contraction Type ◽  
Well Posed ◽  
Rational Type

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.

scholarly journals Fixed Points of Geraghty-Type Mappings in Various Generalized Metric Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-13 ◽  
Author(s):  
Dušan Ðukić ◽  
Zoran Kadelburg ◽  
Stojan Radenović
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Partial Metric ◽  
Generalized Metric Spaces ◽  
Generalized Metric ◽  
Partial Metric Spaces ◽  
Type Spaces

Fixed point theorems for mappings satisfying Geraghty-type contractive conditions are proved in the frame of partial metric spaces, ordered partial metric spaces, and metric-type spaces. Examples are given showing that these results are proper extensions of the existing ones.

Fixed point theorems for expansive mappings in Gp-metric spaces

2017 ◽  
Vol 26 (3) ◽  
pp. 297-308
Author(s):  
MELTEM KAYA ◽  
◽  
HASAN FURKAN ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Partial Metric ◽  
Expansive Mapping ◽  
Partial Metric Spaces ◽  
Weak Compatibility

In the present paper, we adopt the concept of expansive mapping in the context of Gp-metric spaces in a similar manner expansive mapping in metric spaces. Furthermore, we obtain some results on fixed points of expansive type mappings. Also, we prove some common fixed point results for expansive mappings by using the notion of weak compatibility in Gp-metric space. Our results generalize some comparable results in metric spaces and partial metric spaces to Gp-metric spaces. Moreover, some examples are introduced in order to support our new results.

scholarly journals Some related fixed point theorems for multivalued mappings on two metric spaces

2020 ◽  
Vol 12 (2) ◽  
pp. 392-400
Author(s):  
Ö. Biçer ◽  
M. Olgun ◽  
T. Alyildiz ◽  
I. Altun
Keyword(s):  
Fixed Point ◽  
Classical Result ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Multivalued Mappings ◽  
Compact Set ◽  
Complete Metric Spaces ◽  
Bounded Set ◽  
Contraction Type ◽  
Definition Of

The definition of related mappings was introduced by Fisher in 1981. He proved some theorems about the existence of fixed points of single valued mappings defined on two complete metric spaces and relations between these mappings. In this paper, we present some related fixed point results for multivalued mappings on two complete metric spaces. First we give a classical result which is an extension of the main result of Fisher to the multivalued case. Then considering the recent technique of Wardowski, we provide two related fixed point results for both compact set valued and closed bounded set valued mappings via $F$-contraction type conditions.

scholarly journals Fixed point theorems in partial metric spaces with an application

Filomat ◽  
2013 ◽  
Vol 27 (4) ◽  
pp. 617-624
Author(s):  
H.P. Masiha ◽  
F. Sabetghadam ◽  
N. Shahzad
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Partial Metric Space ◽  
Partial Metric ◽  
Fractional Boundary Value Problem ◽  
Partial Metric Spaces ◽  
Contractive Type ◽  
Ordered Partial Metric Space ◽  
Weakly Contractive

Matthews [12] introduced a new distance P on a nonempty set X, which he called a partial metric. The purpose of this paper is to present some fixed point results for weakly contractive type mappings in ordered partial metric space. An application to nonlinear fractional boundary value problem is also presented.

scholarly journals Relation Theoretic Common Fixed Point Results for Generalized Weak Nonlinear Contractions with an Application

Axioms ◽  
2019 ◽  
Vol 8 (2) ◽  
pp. 49 ◽  
Author(s):  
Atiya Perveen ◽  
Idrees A. Khan ◽  
Mohammad Imdad
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Integral Equations ◽  
Binary Relation ◽  
Metric Spaces ◽  
Partial Metric ◽  
System Of Integral Equations ◽  
Partial Metric Spaces ◽  
Nonlinear Contractions

In this paper, by introducing the concept of generalized Ćirić-type weak ( ϕ g , R ) -contraction, we prove some common fixed point results in partial metric spaces endowed with binary relation R . We also deduce some useful consequences showing the usability of our results. Finally, we present an application to establish the solution of a system of integral equations.

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