scholarly journals On Controlled Rectangular Metric Spaces and an Application

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Nayab Alamgir ◽  
Quanita Kiran ◽  
Hassen Aydi ◽  
Yaé Ulrich Gaba
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fredholm Integral Equation ◽  
Metric Spaces ◽  
Real Life ◽  
Real Life Problem

In this paper, we introduce the notion of controlled rectangular metric spaces as a generalization of rectangular metric spaces and rectangular b -metric spaces. Further, we establish some related fixed point results. Our main results extend many existing ones in the literature. The obtained results are also illustrated with the help of an example. In the last section, we apply our results to a common real-life problem in a general form by getting a solution for the Fredholm integral equation in the setting of controlled rectangular metric spaces.

scholarly journals Extended Rectangular Mrc-Metric Spaces and Fixed Point Results

Mathematics ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 1136 ◽  
Author(s):  
Asim ◽  
Nisar ◽  
Morsy ◽  
Imdad
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fredholm Integral Equation ◽  
Metric Spaces ◽  
Banach Contraction Principle ◽  
Uniqueness Of Solution ◽  
Contraction Principle ◽  
Banach Contraction

In this paper, we enlarge the classes of rectangular Mb-metric spaces and extendedrectangular b-metric spaces by considering the class of extended rectangular Mrc-metric spacesand utilize the same to prove an analogue of Banach contraction principle in such spaces. We adoptan example to highlight the utility of our main result. Finally, we apply our result to examine theexistence and uniqueness of solution for a system of Fredholm 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.

scholarly journals Unique Fixed-Point Results in Fuzzy Metric Spaces with an Application to Fredholm Integral Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Iqra Shamas ◽  
Saif Ur Rehman ◽  
Hassen Aydi ◽  
Tayyab Mahmood ◽  
Eskandar Ameer
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Integral Equations ◽  
Fredholm Integral Equation ◽  
Metric Spaces ◽  
Unique Fixed Point ◽  
Fredholm Integral Equations ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Contractive Type

This paper aims at proving some unique fixed-point results for different contractive-type self-mappings in fuzzy metric spaces by using the “triangular property of the fuzzy metric”. Some illustrative examples are presented to support our results. Moreover, we present an application by resolving a particular case of a Fredholm integral equation of the second kind.

scholarly journals Solving a Nonlinear Fredholm Integral Equation via an Orthogonal Metric

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Arul Joseph Gnanaprakasam ◽  
Gunaseelan Mani ◽  
Vahid Parvaneh ◽  
Hassen Aydi
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fredholm Integral Equation ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Complete Metric Spaces ◽  
Nonlinear Fredholm Integral Equation

In this paper, we prove fixed point theorems using orthogonal triangular α -admissibility on orthogonal complete metric spaces. Some of the well-known outcomes in the literature are generalized and expanded by the obtained results. An instance to help our outcome is being presented.

EXISTENCE OF SOLUTION FOR A VOLTERRA TYPE INTEGRAL EQUATION USING DARBO-TYPE F-CONTRACTION

2021 ◽  
Vol 10 (6) ◽  
pp. 2687-2710
Author(s):  
F. Akutsah ◽  
A. A. Mebawondu ◽  
O. K. Narain
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Existence Of Solution ◽  
Volterra Type ◽  
Complete Metric Spaces ◽  
Type Integral ◽  
New Type

In this paper, we provide some generalizations of the Darbo's fixed point theorem and further develop the notion of $F$-contraction introduced by Wardowski in (\cite{wad}, D. Wardowski, \emph{Fixed points of a new type of contractive mappings in complete metric spaces,} Fixed Point Theory and Appl., 94, (2012)). To achieve this, we introduce the notion of Darbo-type $F$-contraction, cyclic $(\alpha,\beta)$-admissible operator and we also establish some fixed point and common fixed point results for this class of mappings in the framework of Banach spaces. In addition, we apply our fixed point results to establish the existence of solution to a Volterra type integral equation.

scholarly journals A New Approach to the Solution of the Fredholm Integral Equation via a Fixed Point on Extended b-Metric Spaces

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 512 ◽  
Author(s):  
Erdal Karapınar ◽  
Panda Kumari ◽  
Durdana Lateef
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Nash Equilibria ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Real Life ◽  
Point Theory ◽  
New Approach ◽  
Correctness Of Programs

It is very well known that real-life applications of fixed point theory are restricted with the transformation of the problem in the form of f ( x ) = x . (1) The Knaster–Tarski fixed point theorem underlies various approaches of checking the correctness of programs. (2) The Brouwer fixed point theorem is used to prove the existence of Nash equilibria in games. (3) Dlala et al. proposed a solution for magnetic field problems via the fixed point approach.

scholarly journals Fejér monotonicity and fixed point theorems with applications to a nonlinear integral equation in complex valued Banach spaces

2020 ◽  
Vol 21 (1) ◽  
pp. 135
Author(s):  
Godwin Amechi Okeke ◽  
Mujahid Abbas
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Banach Spaces ◽  
Nonlinear Integral Equation ◽  
Metric Spaces ◽  
Banach Algebras ◽  
Cone Metric Spaces ◽  
Nonlinear Operators ◽  
Complex Valued ◽  
Cone Metric

It is our purpose in this paper to prove some fixed point results and Fej´er monotonicity of some faster fixed point iterative sequences generated by some nonlinear operators satisfying rational inequality in complex valued Banach spaces. We prove that results in complex valued Banach spaces are valid in cone metric spaces with Banach algebras. Furthermore, we apply our results in solving certain mixed type VolterraFredholm functional nonlinear integral equation in complex valued Banach spaces.

scholarly journals Numerical Treatment of Fixed Point Applied to the Nonlinear Fredholm Integral Equation

2009 ◽  
Vol 2009 (1) ◽  
pp. 735638 ◽  
Author(s):  
MI Berenguer ◽  
MV Fernández Muñoz ◽  
AI Garralda Guillem ◽  
M Ruiz Galán
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fredholm Integral Equation ◽  
Numerical Treatment ◽  
Nonlinear Fredholm Integral Equation

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 Fixed Points for Multivalued Weighted Mean Contractions in a Symmetric Generalized Metric Space

Symmetry ◽  
2020 ◽  
Vol 12 (1) ◽  
pp. 134 ◽  
Author(s):  
Bucur
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Metric Spaces ◽  
Existence Theorems ◽  
Real Life ◽  
Generalized Metric Space ◽  
Weighted Mean ◽  
Generalized Metric Spaces ◽  
Generalized Metric ◽  
New Concepts

This paper defines two new concepts: the concept of multivalued left-weighted mean contractions in the generalized sense of Nadler in a symmetric generalized metric space and the concept of multivalued right-weighted mean contractions in the generalized sense of Nadler in a symmetric generalized metric space, and demonstrates fixed-point theorems for them. For these, we demonstrated two fixed-point existence theorems and their corollaries, by using the properties of the regular-global-inf function and the properties of symmetric generalized metric spaces, respectively. Moreover, we demonstrated that the theorems can be applied in particular cases of inclusion systems. This article contains not only an example of application in science, but also an example of application in real life, in biology, in order to find an equilibrium solution to a prey–predator-type problem. The results of this paper extend theorems for multivalued left-weighted mean contractions in the generalized sense of Nadler, demonstrating that some of the results given by Rus (2008), Mureșan (2002), and Nadler (1969) in metric spaces can also be proved in symmetric generalized metric spaces.

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