scholarly journals MULTIDIMENSIONAL FIXED POINT RESULTS FOR CONTRACTION MAPPING PRINCIPLE WITH APPLICATION

2021 ◽  
pp. 919
Author(s):  
Amrish Handa
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Contraction Mapping ◽  
Metric Spaces ◽  
Complete Metric Space ◽  
Contraction Mapping Principle ◽  
Uniqueness Of The Solution ◽  
Isotone Mappings

The main aim of this article is to study the existence and uniqueness of fixed point for isotone mappings of any number of arguments under contraction mapping principle on a complete metric space endowed with a partial order. As an application of our result we study the existence and uniqueness of the solution to an integral equation. The results we obtain generalize, extend and unify several classical and very recent related results in the literature in metric spaces.

scholarly journals On Fuzzy Contractive Mappings in Fuzzy Metric Spaces

2021 ◽  
Author(s):  
Mohammad Hussein Mohammad Rashid
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Contraction Mapping ◽  
Metric Spaces ◽  
Random Operator ◽  
Random Solution ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Contractive Mappings

Abstract In this paper we introduce a new fuzzy contraction mapping and prove that such mappings have fixed point in $\tau$-complete fuzzy metric spaces. As an application, we shall utilize the results obtained to show the existence and uniqueness of random solution for the following random linear random operator equation. Moreover, we shall show that the existence and uniqueness of the solutions for nonlinear Volterra integral equations on a kind of particular fuzzy metric space.

scholarly journals Generalizations of the Converse of the Contraction Mapping Principle

1966 ◽  
Vol 18 ◽  
pp. 1095-1104 ◽  
Author(s):  
James S. W. Wong
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Contraction Mapping ◽  
Unique Fixed Point ◽  
Complete Metric Space ◽  
Contraction Mapping Principle ◽  
Converse Statement ◽  
Natural Formulation

This paper is an outgrowth of studies related to the converse of the contraction mapping principle. A natural formulation of the converse statement may be stated as follows: “Let X be a complete metric space, and T be a mapping of X into itself such that for each x ∈ X, the sequence of iterates ﹛Tnx﹜ converges to a unique fixed point ω ∈ X. Then there exists a complete metric in X in which T is a contraction.” This is in fact true, even in a stronger sense, as may be seen from the following result of Bessaga (1).

scholarly journals The Existence and Uniqueness of the Solution of a Nonlinear Fredholm–Volterra Integral Equation with Modified Argument via Geraghty Contractions

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 29
Author(s):  
Maria Dobriţoiu
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Integral Equations ◽  
Volterra Integral Equation ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Nonlinear Integral Equations ◽  
Uniqueness Of The Solution

Using some of the extended fixed point results for Geraghty contractions in b-metric spaces given by Faraji, Savić and Radenović and their idea to apply these results to nonlinear integral equations, in this paper we present some existence and uniqueness conditions for the solution of a nonlinear Fredholm–Volterra integral equation with a modified argument.

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 Some fuzzy common fixed point theorems using common limit in the range property with an application

2020 ◽  
Vol 24 (2) ◽  
pp. 33-49
Author(s):  
Ved Bhardwaj ◽  
Kamal Wadhwa
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Common Limit ◽  
Uniqueness Of The Solution ◽  
Common Fixed Point Theorems

In the present paper, we prove some common fixed point theorems for mappings satisfying common limit in the range property in M-fuzzy metric space. Further, we prove fixed point theorem for ph-contractive conditions in aforesaid spaces with the illustration of an example. As an application of our result, we study the existence and uniqueness of the solution of integral equation (Volterra integral equations of the second kind) with instances.

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.

scholarly journals Fixed Points Results in G-Metric Spaces

2019 ◽  
Vol 32 (1) ◽  
pp. 142
Author(s):  
Salwa Salman Abed ◽  
Anaam Neamah Faraj ◽  
Anaam Neamah Faraj
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Space ◽  
Contraction Mapping ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Complete Metric Space ◽  
Closed Ball ◽  
Local Contraction

  In this paper, the concept of contraction mapping on a -metric space is extended with a consideration on local contraction.  As a result, two fixed point theorems were proved for contraction on a closed ball in a complete -metric space.

scholarly journals New Fixed Point Results via (θ,ψ)R-Weak Contractions with an Application

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 887
Author(s):  
Mohammad Imdad ◽  
Based Ali ◽  
Waleed M. Alfaqih ◽  
Salvatore Sessa ◽  
Abdullah Aldurayhim
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Volterra Type ◽  
Auxiliary Functions ◽  
Type Integral ◽  
Uniqueness Of The Solution

In this paper, inspired by Jleli and Samet (Journal of Inequalities and Applications 38 (2014) 1–8), we introduce two new classes of auxiliary functions and utilize the same to define ( θ , ψ ) R -weak contractions. Utilizing ( θ , ψ ) R -weak contractions, we prove some fixed point theorems in the setting of relational metric spaces. We employ some examples to substantiate the utility of our newly proven results. Finally, we apply one of our newly proven results to ensure the existence and uniqueness of the solution of a Volterra-type integral equation.

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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