scholarly journals Fixed Point Theorems for Kannan Contractions and Weakly Contractive Mappings on a Modular Metric Space Endowed with a Graph

2017 ◽  
Vol 14 (1) ◽  
pp. 77-85
Author(s):  
Prerna Pathak ◽  
◽  
Aklesh Pariya ◽  
V. H. Badshah ◽  
Nirmala Gupta ◽  
...  
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Modular Metric Space ◽  
Contractive Mappings ◽  
Weakly Contractive

scholarly journals Relation-Theoretic Fixed Point Theorems for Generalized Weakly Contractive Mappings

Symmetry ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 29
Author(s):  
Priyam Chakraborty ◽  
Binayak S. Choudhury ◽  
Manuel De la Sen
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Fixed Point Theory ◽  
Point Theory ◽  
The Other ◽  
Binary Relations ◽  
Contractive Mappings ◽  
Fixed Point Result ◽  
Weakly Contractive

In recent times there have been two prominent trends in metric fixed point theory. One is the use of weak contractive inequalities and the other is the use of binary relations. Combining the two trends, in this paper we establish a relation-theoretic fixed point result for a mapping which is defined on a metric space with an arbitrary binary relation and satisfies a weak contractive inequality for any pair of points whenever the pair of points is related by a given relation. The uniqueness is obtained by assuming some extra conditions. The metric space is assumed to be R -complete. We use R -continuity of functions. The property of local T-transitivity of the relation R is used in the main theorem. There is an illustrative example. An existing fixed point result is generalized through the present work. We use a method in the proof of our main theorem which is a blending of relation-theoretic and analytic approaches.

Meir–Keeler type contractive mappings in modular and partial modular metric spaces

2019 ◽  
Vol 13 (05) ◽  
pp. 2050087
Author(s):  
Hasan Hosseinzadeh ◽  
Vahid Parvaneh
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Ordered Metric Spaces ◽  
Modular Metric Space ◽  
Partially Ordered Metric Spaces ◽  
Partially Ordered ◽  
Modular Metric Spaces ◽  
Contractive Mappings

In this paper, first, we introduce the class of [Formula: see text]-Meir–Keeler contractive mappings and establish some fixed point results. Next, we introduce the notion of partial modular metric space and establish some fixed point results in this new spaces. As consequences of these results, we deduce some fixed point theorems in modular metric spaces endowed with a graph and in partially ordered metric spaces. Some examples are furnished to demonstrate the validity of the obtained results.

scholarly journals Generalised Presic Type Operators in Modular Metric Space and an Application to Integral Equations of Caratheodory Type Functions

2021 ◽  
Vol 2021 ◽  
pp. 1-20
Author(s):  
Fahad Sameer Alshammari ◽  
K. P. Reshma ◽  
Rajagopalan R. ◽  
Reny George
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Modular Metric Space ◽  
Contractive Mappings ◽  
Modular Spaces ◽  
Type Integral ◽  
Fixed Point Equation ◽  
Point Equation

Extending the Presic type operators to modular spaces, we introduce generalised Presic type w -contractive mappings and strongly w -contractive mappings in a modular metric space and establish fixed-point theorems for such contractions in modular spaces. Ulam–Hyers stability of the fixed-point equation involving Presic type operators is also discussed. Our results extend and generalise some known results in the literature. The results are supported by appropriate example and an application to Caratheodory type integral equation.

scholarly journals Fixed point theorems for weakly contractive mappings on a metric space endowed with a graph

Filomat ◽  
2014 ◽  
Vol 28 (3) ◽  
pp. 441-450 ◽  
Author(s):  
Maria Samreen ◽  
Tayyab Kamran
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Contractive Mappings ◽  
Weakly Contractive

In this paper we define the notion of weakly G-contractive mappings and obtain some fixed point theorems for such mappings. Our theorems generalize, extend and unify some recent results by Harjani and Sadarangani and those contained therein. Moreover, we also furnish with an application and an example to substantiate the validity of our results.

Fixed point theorems for generalized weakly contractive mappings

2011 ◽  
Vol 74 (6) ◽  
pp. 2116-2126 ◽  
Author(s):  
Binayak S. Choudhury ◽  
P. Konar ◽  
B.E. Rhoades ◽  
N. Metiya
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Contractive Mappings ◽  
Weakly Contractive

scholarly journals Extended partial b-metric spaces and some fixed point results

Filomat ◽  
2018 ◽  
Vol 32 (8) ◽  
pp. 2837-2850 ◽  
Author(s):  
V. Parvaneh ◽  
Z. Kadelburg
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Metric Space ◽  
Metric Spaces ◽  
Volterra Type ◽  
Fundamental Lemma ◽  
Contractive Mappings ◽  
Type Integral ◽  
Convergence Of Sequences ◽  
Weakly Contractive

In this paper, we introduce the concept of extended partial b-metric space. We demonstrate a fundamental lemma for the convergence of sequences in such spaces. Then we prove some fixed point results for weakly contractive mappings in the setup of ordered extended partial b-metric spaces. An example is given to verify the effectiveness and applicability of our main results. An application of these results to Volterra-type integral equations is provided at the end.

scholarly journals TEOREMA TITIK TETAP UNTUK PEMETAAN KANNAN PADA RUANG METRIK MODULAR TERITLAK

1970 ◽  
Vol 11 (2) ◽  
pp. 11
Author(s):  
Lusi Harini
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Modular Metric Space ◽  
Type Mapping ◽  
Kannan Mapping ◽  
Finite Set

In this paper, we will discuss about fixed point theorems in generalized modular metric space for Kannan-  type mapping. The existence of the fixed point of this mapping is guaranteed by providing that the mapping domain is a -finite set and the Kannan-  mapping constant  satisfied  where K is a constant from the axiom of generalized modular metric space.

scholarly journals On ParametricS-Metric Spaces and Fixed-Point Type Theorems for Expansive Mappings

2016 ◽  
Vol 2016 ◽  
pp. 1-6 ◽  
Author(s):  
Nihal Taş ◽  
Nihal Yılmaz Özgür
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contractive Mappings ◽  
Point Type

We introduce the notion of a parametricS-metric space as generalization of a parametric metric space. Using some expansive mappings, we prove a fixed-point theorem on a parametricS-metric space. It is important to obtain new fixed-point theorems on a parametricS-metric space because there exist some parametricS-metrics which are not generated by any parametric metric. We expect that many mathematicians will study various fixed-point theorems using new expansive mappings (or contractive mappings) in a parametricS-metric space.

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