scholarly journals On a New Generalization of Banach Contraction Principle with Application

Mathematics ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 862 ◽  
Author(s):  
Hüseyin Işık ◽  
Babak Mohammadi ◽  
Mohammad Reza Haddadi ◽  
Vahid Parvaneh
Keyword(s):  
Fixed Point ◽  
Banach Contraction Principle ◽  
Contraction Principle ◽  
Current Work ◽  
Fixed Point Result ◽  
Banach Contraction ◽  
The Banach Contraction Principle

The main purpose of the current work is to present firstly a new generalization of Caristi’s fixed point result and secondly the Banach contraction principle. An example and an application is given to show the usability of our results.

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 Meir-Keeler Type Common Fixed Point Result in Dislocated Metric Space

2018 ◽  
Vol 1 (2) ◽  
pp. 53-59
Author(s):  
Dinesh Panthi
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Banach Contraction Principle ◽  
Fixed Point Result ◽  
Dislocated Metric Space ◽  
Banach Contraction ◽  
Strict Contraction ◽  
Dislocated Metric ◽  
The Banach Contraction Principle

Meir and E. Keeler [11] generalized the Banach Contraction Principle [1] with the notion of weakly uniformly strict contraction which is famous as a (ε - δ) contraction. In this article, we establish a Meir- Keeler type common fixed point result in dislocated metric space which generalize and extend similar fixed point results in the literature.

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 Wardowski Type Characterization of the Interpolative Berinde Weak Fixed Point Theorem

2020 ◽  
pp. 411-414
Author(s):  
Clement Boateng Ampadu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Banach Contraction Principle ◽  
Contraction Principle ◽  
Weak Contraction ◽  
Banach Contraction ◽  
The Banach Contraction Principle

In [1], Wardowski introduced the F-contractions, and used it to prove the Banach contraction principle. In this paper we introduce a concept of F-interpolative Berinde weak contraction, and use it to prove the interpolative Berinde weak mapping theorem of [2].

scholarly journals A generalization of Nadler fixed point theorem

2015 ◽  
Vol 31 (3) ◽  
pp. 403-410
Author(s):  
FRANCESCA VETRO ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Metric Spaces ◽  
Banach Contraction Principle ◽  
Contraction Principle ◽  
Multivalued Mappings ◽  
Contractive Condition ◽  
Complete Metric Spaces ◽  
Banach Contraction ◽  
The Banach Contraction Principle

Jleli and Samet gave a new generalization of the Banach contraction principle in the setting of Branciari metric spaces [Jleli, M. and Samet, B., A new generalization of the Banach contraction principle, J. Inequal. Appl., 2014:38 (2014)]. The purpose of this paper is to study the existence of fixed points for multivalued mappings, under a similar contractive condition, in the setting of complete metric spaces. Some examples are provided to illustrate the new theory.

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).

A generalization of the Banach contraction principle in noncomplete metric spaces

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3357-3363
Author(s):  
Tomonari Suzuki
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Fixed Point Property ◽  
Banach Contraction Principle ◽  
Contraction Principle ◽  
Sufficient Condition ◽  
Point Property ◽  
Banach Contraction ◽  
The Banach Contraction Principle

We give a sufficient condition on metric spaces possessing the Banach fixed point property (BFPP). Further we also give a sufficient condition on not possessing BFPP.

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