scholarly journals On Some New Results in Graphical Rectangular b-Metric Spaces

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 488
Author(s):  
Pravin Baradol ◽  
Jelena Vujaković ◽  
Dhananjay Gopal ◽  
Stojan Radenović
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Banach Contraction Principle ◽  
Contraction Principle ◽  
Banach Contraction ◽  
The Banach Contraction Principle

In this paper, we provide an approach to establish the Banach contraction principle ( for the case λ ∈ [ 0 , 1 ) ) , Edelstein, Reich, and Meir–Keeler type contractions in the context of graphical rectangular b-metric space. The obtained results not only enrich and improve recent fixed point theorems of this new metric spaces but also provide positive answers to the questions raised by Mudasir Younis et al. (J. Fixed Point Theory Appl., doi:10.1007/s11784-019-0673-3, 2019).

scholarly journals Fixed point theorems in preordered sets

2021 ◽  
Vol 23 (4) ◽  
Author(s):  
Jarosław Górnicki
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Banach Contraction Principle ◽  
Ordered Metric Spaces ◽  
Banach Contraction ◽  
Preordered Sets ◽  
The Banach Contraction Principle

AbstractRan and Reurings (Proc Am Math Soc 132(5):1435–1443, 2003) extended the Banach contraction principle to the setting of partially ordered metric spaces and recently Proinov (J Fixed Point Theory Appl 22:21, 2020) extended and unified many earlier fixed point theorems. In this paper we will present analogous results for the significantly wider class of mappings on preordered metric spaces. We give non-trivial examples of Kannan-type mappings.

scholarly journals Fixed-Point Theorems for θ − ϕ -Contraction in Generalized Asymmetric Metric Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-19
Author(s):  
Abdelkarim Kari ◽  
Mohamed Rossafi ◽  
Hamza Saffaj ◽  
El Miloudi Marhrani ◽  
Mohamed Aamri
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Banach Contraction Principle ◽  
Contraction Principle ◽  
Banach Contraction ◽  
The Banach Contraction Principle

In the last few decades, a lot of generalizations of the Banach contraction principle had been introduced. In this paper, we present the notion of θ -contraction and θ − ϕ -contraction in generalized asymmetric metric spaces to study the existence and uniqueness of the fixed point for them. We will also provide some illustrative examples. Our results improve many existing results.

scholarly journals Some New Fixed Point Theorems in Complex ValuedG-Metric Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Ing-Jer Lin ◽  
Wei-Shih Du ◽  
Qiao-Feng Zheng
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Banach Contraction Principle ◽  
Contraction Principle ◽  
Banach Contraction ◽  
Complex Valued ◽  
The Banach Contraction Principle

Some new fixed point theorems are established in the setting of complex valuedG-metric spaces. These new results improve and generalize Kang et al.’s results, the Banach contraction principle, and some well-known results in the literature.

scholarly journals On Fixed Point Results for Modified JS-Contractions with Applications

Axioms ◽  
2019 ◽  
Vol 8 (3) ◽  
pp. 84 ◽  
Author(s):  
Vahid Parvaneh ◽  
Nawab Hussain ◽  
Aiman Mukheimer ◽  
Hassen Aydi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Banach Contraction Principle ◽  
Contraction Principle ◽  
Contractive Condition ◽  
Contractive Mappings ◽  
Control Functions ◽  
Banach Contraction ◽  
The Banach Contraction Principle

In [Fixed Point Theory Appl., 2015 (2015):185], the authors introduced a new concept of modified contractive mappings, generalizing Ćirić, Chatterjea, Kannan, and Reich type contractions. They applied the condition ( θ 4 ) (see page 3, Section 2 of the above paper). Later, in [Fixed Point Theory Appl., 2016 (2016):62], Jiang et al. claimed that the results in [Fixed Point Theory Appl., 2015 (2015):185] are not real generalizations. In this paper, by restricting the conditions of the control functions, we obtain a real generalization of the Banach contraction principle (BCP). At the end, we introduce a weakly JS-contractive condition generalizing the JS-contractive condition.

scholarly journals A note on fixed point theorems in metric spaces

2015 ◽  
Vol 31 (1) ◽  
pp. 127-134
Author(s):  
DARIUSZ WARDOWSKI ◽  
◽  
NGUYEN VAN DUNG ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Banach Contraction Principle ◽  
Contraction Principle ◽  
Banach Contraction ◽  
The Banach Contraction Principle

In this paper, we show that the existence of fixed points in some known fixed point theorems in the literature is a consequence of the Banach contraction principle.

scholarly journals Banach Contraction Principle and Meir–Keeler Type of Fixed Point Theorems for Pre-Metric Spaces

Axioms ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 57
Author(s):  
Hsien-Chung Wu
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Main Issue ◽  
Banach Contraction Principle ◽  
Contraction Principle ◽  
Banach Contraction

The fixed point theorems in so-called pre-metric spaces is investigated in this paper. The main issue in the pre-metric space is that the symmetric condition is not assumed to be satisfied, which can result in four different forms of triangle inequalities. In this case, the fixed point theorems in pre-metric space will have many different styles based on the different forms of triangle inequalities.

scholarly journals COINCIDENCE AND COMMON FIXED POINT THEOREMS IN Ƒ-METRIC SPACES

2020 ◽  
Vol 4 (3) ◽  
pp. 43-49
Author(s):  
Demet Binbaşıoğlu
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Banach Contraction Principle ◽  
Contraction Principle ◽  
Natural Topology ◽  
Banach Contraction ◽  
Common Fixed Point Theorems

Recently, the concept of Ƒ metric space has been introduced and have been defined a natural topology in this spaces by Jleli and Samet[6]. Furthermore, a new style of Banach contraction principle has been given in the Ƒ metric spaces. In this paper, we prove some coincidence and common fixed point theorems in Ƒ metric spaces.

scholarly journals New Fixed Point Theorems for θ ‐ ϕ -Contraction on Rectangular b -Metric Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Abdelkarim Kari ◽  
Mohamed Rossafi ◽  
El Miloudi Marhrani ◽  
Mohamed Aamri
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Banach Contraction Principle ◽  
Contraction Principle ◽  
Banach Contraction ◽  
The Banach Contraction Principle

The Banach contraction principle is the most celebrated fixed point theorem and has been generalized in various directions. In this paper, inspired by the concept of θ ‐ ϕ -contraction in metric spaces, introduced by Zheng et al., we present the notion of θ ‐ ϕ -contraction in b -rectangular metric spaces and study the existence and uniqueness of a fixed point for the mappings in this space. Our results improve many existing results.

scholarly journals A New Kind of Nonlinear Quasicontractions in Metric Spaces

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 661 ◽  
Author(s):  
Nicolae-Adrian Secelean
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Metric Spaces ◽  
Sufficient Conditions ◽  
Banach Contraction Principle ◽  
Contraction Principle ◽  
Banach Contraction ◽  
The Banach Contraction Principle

Starting from two extensions of the Banach contraction principle due to Ćirić (1974) and Wardowski (2012), in the present paper we introduce the concepts of Ćirić type ψ F -contraction and ψ F -quasicontraction on a metric space and give some sufficient conditions under which the respective mappings are Picard operators. Some known fixed point results from the literature can be obtained as particular cases.

Fuzzy double controlled metric spaces and related results

2021 ◽  
Vol 40 (5) ◽  
pp. 9977-9985
Author(s):  
Naeem Saleem ◽  
Hüseyin Işık ◽  
Salman Furqan ◽  
Choonkil Park
Keyword(s):  
Integral Equation ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Banach Contraction Principle ◽  
Uniqueness Of Solution ◽  
Contraction Principle ◽  
Triangular Inequality ◽  
Banach Contraction ◽  
The Banach Contraction Principle

In this paper, we introduce the concept of fuzzy double controlled metric space that can be regarded as the generalization of fuzzy b-metric space, extended fuzzy b-metric space and controlled fuzzy metric space. We use two non-comparable functions α and β in the triangular inequality as: M q ( x , z , t α ( x , y ) + s β ( y , z ) ) ≥ M q ( x , y , t ) ∗ M q ( y , z , s ) . We prove Banach contraction principle in fuzzy double controlled metric space and generalize the Banach contraction principle in aforementioned spaces. We give some examples to support our main results. An application to existence and uniqueness of solution for an integral equation is also presented in this work.

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