scholarly journals Fixed Point Theorems for Mizoguchi-Takahashi Type Contraction in Bicomplex-Valued Metric Spaces and Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Fuli He ◽  
Z. Mostefaoui ◽  
M. Abdalla
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Nonlinear Integral Equation ◽  
Metric Spaces ◽  
Banach Contraction ◽  
Uniqueness Of The Solution ◽  
Contractive Maps ◽  
The Banach Contraction Principle ◽  
Type Contraction

The main aim of this paper is to study and establish some new fixed point theorems for contractive maps that satisfied Mizoguchi-Takahashi’s condition in the setting of bicomplex-valued metric spaces. These new results improve and generalize the Banach contraction principle and some well-known results in the literature. Finally, as applications of our results, we give the existence and uniqueness of the solution of a nonlinear integral equation.

scholarly journals Fixed Points and Continuity for a Pair of Contractive Maps with Application to Nonlinear Volterra Integral Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Santosh Kumar
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Volterra Integral Equations ◽  
Discontinuous Mappings ◽  
Contractive Maps ◽  
Uniqueness Of A Solution ◽  
Type Contraction

In this paper, we have established and proved fixed point theorems for the Boyd-Wong-type contraction in metric spaces. In particular, we have generalized the existing results for a pair of mappings that possess a fixed point but not continuous at the fixed point. We can apply this result for both continuous and discontinuous mappings. We have concluded our results by providing an illustrative example for each case and an application to the existence and uniqueness of a solution of nonlinear Volterra integral equations.

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 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.

A generalization of Reich’s fixed point theorem for multi-valued mappings

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3295-3305 ◽  
Author(s):  
Antonella Nastasi ◽  
Pasquale Vetro
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contractive Condition ◽  
Complete Metric Spaces ◽  
New Class ◽  
Banach Contraction ◽  
The Banach Contraction Principle

Motivated by a problem concerning multi-valued mappings posed by Reich [S. Reich, Some fixed point problems, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 57 (1974) 194-198] and a paper of Jleli and Samet [M. Jleli, B. Samet, A new generalization of the Banach contraction principle, J. Inequal. Appl. 2014:38 (2014) 1-8], we consider a new class of multi-valued mappings that satisfy a ?-contractive condition in complete metric spaces and prove some fixed point theorems. These results generalize Reich?s and Mizoguchi-Takahashi?s fixed point theorems. Some examples are given to show the usability of the obtained 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 Recent Fixed-Point Results for θ − Contraction Mappings in Rectangular M − Metric Spaces with Supportive Application

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Mustafa Mudhesh ◽  
Hasanen A. Hammad ◽  
Habes Alsamir ◽  
Muhammad Arshad ◽  
Eskandar Ameer
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Theoretical Result ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Nonlinear Integral Equation ◽  
Metric Spaces ◽  
Contraction Mappings ◽  
Uniqueness Of The Solution

The goal of this manuscript is to present a new fixed-point theorem on θ − contraction mappings in the setting of rectangular M-metric spaces (RMMSs). Also, a nontrivial example to illustrate our main result has been given. Moreover, some related sequences with θ − contraction mappings have been discussed. Ultimately, our theoretical result has been implicated to study the existence and uniqueness of the solution to a nonlinear integral equation (NIE).

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 New Fixed Point Theorems in Orthogonal F -Metric Spaces with Application to Fractional Differential Equation

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 832
Author(s):  
Tanzeela Kanwal ◽  
Azhar Hussain ◽  
Hamid Baghani ◽  
Manuel de la Sen
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Periodic Point ◽  
Fractional Differential Equation ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Nonlinear Fractional Differential Equation ◽  
Uniqueness Of The Solution ◽  
Fractional Differential

We present the notion of orthogonal F -metric spaces and prove some fixed and periodic point theorems for orthogonal ⊥ Ω -contraction. We give a nontrivial example to prove the validity of our result. Finally, as application, we prove the existence and uniqueness of the solution of a nonlinear fractional differential equation.

scholarly journals C⁎-Algebra-Valued G-Metric Spaces and Related Fixed-Point Theorems

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Congcong Shen ◽  
Lining Jiang ◽  
Zhenhua Ma
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
C Algebra ◽  
Uniqueness Of The Solution

We introduce the notion of the C⁎-algebra-valued G-metric space. The existence and uniqueness of some fixed-point theorems for self-mappings with contractive or expansive conditions on complete C⁎-algebra-valued G-metric spaces are proved. As an application, we prove the existence and uniqueness of the solution of a type of differential equations.

scholarly journals Solving an Integral Equation by Using Fixed Point Approach in Fuzzy Bipolar Metric Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Gunaseelan Mani ◽  
Arul Joseph Gnanaprakasam ◽  
Absar Ul Haq ◽  
Fahd Jarad ◽  
Imran Abbas Baloch
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Existence And Uniqueness ◽  
Nonlinear Integral Equation ◽  
Metric Spaces ◽  
Fixed Point Approach ◽  
Uniqueness Of The Solution ◽  
Theoretical Results

The purpose of this manuscript is to obtain some fixed point results under mild contractive conditions in fuzzy bipolar metric spaces. Our results generalize and extend many of the previous findings in the same approach. Moreover, two examples to support our theorems are obtained. Finally, to examine and strengthen the theoretical results, the existence and uniqueness of the solution to a nonlinear integral equation was studied as a kind of applications.

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