scholarly journals Application of Banach Contraction Principle in Complex Valued Rectangular b-Metric Space

2020 ◽  
Vol 1490 ◽  
pp. 012003
Author(s):  
Sunarsini ◽  
Aufa Biahdillah ◽  
Sentot Didik Surjanto
Keyword(s):  
Metric Space ◽  
Banach Contraction Principle ◽  
Contraction Principle ◽  
Banach Contraction ◽  
Complex Valued

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.

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 Caristi Fixed Point Theorem in Metric Spaces with a Graph

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
M. R. Alfuraidan ◽  
M. A. Khamsi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Metric Spaces ◽  
Banach Contraction Principle ◽  
Contraction Principle ◽  
Caristi’S Fixed Point Theorem ◽  
Banach Contraction ◽  
Caristi's Fixed Point Theorem

We discuss Caristi’s fixed point theorem for mappings defined on a metric space endowed with a graph. This work should be seen as a generalization of the classical Caristi’s fixed point theorem. It extends some recent works on the extension of Banach contraction principle to metric spaces with graph.

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 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 Best Proximity Point Results in b-Metric Space and Application to Nonlinear Fractional Differential Equation

Mathematics ◽  
2018 ◽  
Vol 6 (11) ◽  
pp. 221 ◽  
Author(s):  
Azhar Hussain ◽  
Tanzeela Kanwal ◽  
Muhammad Adeel ◽  
Stojan Radenović
Keyword(s):  
Differential Equation ◽  
Fractional Differential Equation ◽  
Metric Space ◽  
Best Proximity Point ◽  
American Mathematical Society ◽  
Banach Contraction Principle ◽  
Contraction Principle ◽  
Nonlinear Fractional Differential Equation ◽  
Banach Contraction ◽  
Fractional Differential

Based on the concepts of contractive conditions due to Suzuki (Suzuki, T., A generalized Banach contraction principle that characterizes metric completeness, Proceedings of the American Mathematical Society, 2008, 136, 1861–1869) and Jleli (Jleli, M., Samet, B., A new generalization of the Banach contraction principle, J. Inequal. Appl., 2014, 8 pages), our aim is to combine the aforementioned concepts in more general way for set valued and single valued mappings and to prove the existence of best proximity point results in the context of b-metric spaces. Endowing the concept of graph with b-metric space, we present some best proximity point results. Some concrete examples are presented to illustrate the obtained results. Moreover, we prove the existence of the solution of nonlinear fractional differential equation involving Caputo derivative. Presented results not only unify but also generalize several existing results on the topic in the corresponding literature.

scholarly journals Fixed point results in $M_{\nu }$-metric spaces with an application

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Mohammad Asim ◽  
Izhar Uddin ◽  
Mohammad Imdad
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Metric Space ◽  
Fredholm Integral Equation ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Banach Contraction Principle ◽  
Uniqueness Of Solution ◽  
Contraction Principle ◽  
Banach Contraction

Abstract In this paper, we introduce the concept of $M_{\nu}$ M ν -metric as a generalization of M-metric and ν-generalized metric and also prove an analogue of Banach contraction principle in an $M_{\nu}$ M ν -metric space. Also, we adopt an example to highlight the utility of our main result which extends and improves the corresponding relevant results of the existing literature. Finally, we use our main result to examine the existence and uniqueness of solution for a Fredholm integral equation.

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