scholarly journals A Relation-Theoretic Metrical Fixed Point Theorem for Rational Type Contraction Mapping with an Application

Axioms ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 316
Author(s):  
Asik Hossain ◽  
Faizan Ahmad Khan ◽  
Qamrul Haq Khan
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Contraction Mapping ◽  
Complete Metric Space ◽  
Contractive Mapping ◽  
Linear Integral Equation ◽  
Linear Integral ◽  
Rational Type ◽  
Type Contraction

In this article, we discuss the relation theoretic aspect of rational type contractive mapping to obtain fixed point results in a complete metric space under arbitrary binary relation. Furthermore, we provide an application to find a solution to a non-linear integral equation.

Best approximation and fixed points for rational-type contraction mappings

2019 ◽  
Vol 25 (2) ◽  
pp. 205-209
Author(s):  
Sumit Chandok
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Best Approximation ◽  
Contraction Mapping ◽  
Metric Spaces ◽  
Contraction Mappings ◽  
Invariant Approximation ◽  
Frame Work ◽  
Rational Type ◽  
Type Contraction

AbstractIn this paper, we prove a fixed point theorem for a rational type contraction mapping in the frame work of metric spaces. Also, we extend Brosowski–Meinardus type results on invariant approximation for such class of contraction mappings. The results proved extend some of the known results existing in the literature.

scholarly journals The Newtonian Operator and Global Convergence Balls for Newton’s Method

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1074
Author(s):  
José A. Ezquerro ◽  
Miguel A. Hernández-Verón
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Global Convergence ◽  
Point Theorem ◽  
Newton’S Method ◽  
Newton's Method ◽  
Linear Integral Equation ◽  
The Fixed Point Theorem ◽  
Linear Integral

We obtain results of restricted global convergence for Newton’s method from ideas based on the Fixed-Point theorem and using the Newtonian operator and auxiliary points. The results are illustrated with a non-linear integral equation of Davis-type and improve the results previously given by the authors.

scholarly journals Solving a Class of Integral Equations via Contractive Mapping with Rational Type

2020 ◽  
Vol 13 (4) ◽  
pp. 995-1015
Author(s):  
Abdullah Abdullah ◽  
Muhammad Sarwar ◽  
Zead Mustafa ◽  
Mohammed M.M. Jaradat
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Integral Equations ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Coupled Fixed Point ◽  
Contractive Mapping ◽  
Coupled Fixed Point Theorem ◽  
Set Up ◽  
Rational Type

In this paper, using rational type contractive conditions, the existence and uniqueness of common coupled fixed point theorem in the set up of Gb-metric spaces is studied. The derived result cover and generalize some well-known comparable results in the existing literature. Then we use the derived results to prove the existence and uniqueness solution for some classes of integral equations. Further more, an example of such type of integral equation is presented.

scholarly journals On Pata–Suzuki-Type Contractions

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 720
Author(s):  
Obaid Alqahtani ◽  
Venigalla Madhulatha Himabindu ◽  
Erdal Karapınar
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Point Theorem ◽  
Metric Space ◽  
Complete Metric Space ◽  
Admissible Mapping

In this paper, we aim to obtain fixed-point results by merging the interesting fixed-point theorem of Pata and Suzuki in the framework of complete metric space and to extend these results by involving admissible mapping. After introducing two new contractions, we investigate the existence of a (common) fixed point in these new settings. In addition, we shall consider an integral equation as an application of obtained results.

scholarly journals Fixed Point Results Satisfying Rational Type Contraction inG-Metric Spaces

2016 ◽  
Vol 2016 ◽  
pp. 1-7
Author(s):  
Branislav Z. Popović ◽  
Muhammad Shoaib ◽  
Muhammad Sarwar
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Unique Fixed Point ◽  
Contractive Condition ◽  
Fixed Point Result ◽  
Rational Type ◽  
Type Contraction

A unique fixed point theorem for three self-maps under rational type contractive condition is established. In addition, a unique fixed point result for six continuous self-mappings through rational type expression is also discussed.

scholarly journals Some Rational Coupled Fuzzy Cone Contraction Theorems in Fuzzy Cone Metric Spaces with an Application

2021 ◽  
Vol 2021 ◽  
pp. 1-21
Author(s):  
Saif Ur Rehman ◽  
Muhammad Talha Waheed ◽  
Naeem Jan ◽  
Abdu Gumaei ◽  
Mabrook Al-Rakhami
Keyword(s):  
Fixed Point ◽  
Contraction Mapping ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coupled Fixed Point ◽  
Integral Type ◽  
Cone Metric Spaces ◽  
Cone Metric ◽  
Rational Type ◽  
Type Contraction

In this paper, we establish the new concept of rational coupled fuzzy cone contraction mapping in fuzzy cone metric spaces and prove some unique rational-type coupled fixed-point theorems in the framework of fuzzy cone metric spaces by using “the triangular property of fuzzy cone metric.” To ensure the existence of our results, we present some illustrative unique coupled fixed-point examples. Furthermore, we present an application of a Lebesgue integral-type contraction mapping in fuzzy cone metric spaces and to prove a unique coupled fixed-point theorem.

scholarly journals Several Fixed Point Theorems in Convex b-Metric Spaces and Applications

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 242 ◽  
Author(s):  
Lili Chen ◽  
Chaobo Li ◽  
Radoslaw Kaczmarek ◽  
Yanfeng Zhao
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Strong Convergence ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Iteration Scheme ◽  
Linear Integral Equation ◽  
Iteration Algorithm ◽  
Linear Integral ◽  
Mann’S Iteration

Our paper is devoted to indicating a way of generalizing Mann’s iteration algorithm and a series of fixed point results in the framework of b-metric spaces. First, the concept of a convex b-metric space by means of a convex structure is introduced and Mann’s iteration algorithm is extended to this space. Next, by the help of Mann’s iteration scheme, strong convergence theorems for two types of contraction mappings in convex b-metric spaces are obtained. Some examples supporting our main results are also presented. Moreover, the problem of the T-stability of Mann’s iteration procedure for the above mappings in complete convex b-metric spaces is considered. As an application, we apply our main result to approximating the solution of the Fredholm linear integral equation.

scholarly journals On a fixed point theorem with application to functional equations

2019 ◽  
Vol 17 (1) ◽  
pp. 1724-1736
Author(s):  
Muhammad Nazam ◽  
Muhammad Arshad ◽  
Choonkil Park ◽  
Hasan Mahmood
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Sufficient Conditions ◽  
Partial Metric ◽  
Ordered Metric Spaces ◽  
Partial Metric Spaces ◽  
Rational Type ◽  
Type Contraction

Abstract The purpose of this paper is to study behavior of a rational type contraction introduced in [A fixed point theorem for contractions of rational type in partially ordered metric spaces, Ann. Univ. Ferrara, 2013, 59, 251–258] in context of ordered dualistic partial metric spaces and to investigate sufficient conditions for the existence of a fixed point in this space. These results extend various comparable results, existing in the literature. We give examples to explain our findings. We apply our result to prove the existence of the solution of functional equation.

scholarly journals Fixed point theorem with contractive mapping on C*-Algebra valued G-Metric Space

2021 ◽  
Vol 2106 (1) ◽  
pp. 012015
Author(s):  
A Wijaya ◽  
N Hariadi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Unique Fixed Point ◽  
Complete Metric Space ◽  
Contractive Mapping ◽  
C Algebra ◽  
Metric Function ◽  
Interesting Theorem

Abstract Banach-Caccioppoli Fixed Point Theorem is an interesting theorem in metric space theory. This theorem states that if T : X → X is a contractive mapping on complete metric space, then T has a unique fixed point. In 2018, the notion of C *-algebra valued G-metric space was introduced by Congcong Shen, Lining Jiang, and Zhenhua Ma. The C *-algebra valued G-metric space is a generalization of the G-metric space and the C*-algebra valued metric space, meanwhile the G-metric space and the C *-algebra valued metric space itself is a generalization of known metric space. The G-metric generalized the domain of metric from X × X into X × X × X, the C *-algebra valued metric generalized the codomain from real number into C *-algebra, and the C *-algebra valued G-metric space generalized both the domain and the codomain. In C *-algebra valued G-metric space, there is one theorem that is similar to the Banach-Caccioppoli Fixed Point Theorem, called by fixed point theorem with contractive mapping on C *-algebra valued G-metric space. This theorem is already proven by Congcong Shen, Lining Jiang, Zhenhua Ma (2018). In this paper, we discuss another new proof of this theorem by using the metric function d(x, y) = max{G(x, x, y),G(y, x, x)}.

scholarly journals Common Fixed Point Theorem via Cyclic (α,β)-(ψ,φ)S-Contraction with Applications

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 198
Author(s):  
Mian Zada ◽  
Muhammad Sarwar ◽  
Fahd Jarad ◽  
Thabet Abdeljawad
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Functional Equations ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Common Fixed Point Theorems ◽  
Common Fixed Point Theorem ◽  
Rational Type ◽  
Type Contraction

In this paper, we introduce the notion of cyclic ( α , β ) - ( ψ , φ ) s -rational-type contraction in b-metric spaces, and using this contraction, we prove common fixed point theorems. Our work generalizes many existing results in the literature. In order to highlight the usefulness of our results, applications to functional equations are given.

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