scholarly journals On the existence and uniqueness of the solution of a nonlinear integral equation

2019 ◽  
Vol 488 (6) ◽  
pp. 595-598
Author(s):  
M. V. Nikolaev ◽  
A. A. Nikitin
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Integral Operator ◽  
Spatial Model ◽  
Existence And Uniqueness ◽  
Nonlinear Integral Equation ◽  
Sufficient Conditions ◽  
Biological Communities ◽  
Uniqueness Of The Solution

In this paper we study the nonlinear integral equation that arose in the spatial model of biological communities developed by Austrian scientists Ulf Dieckmann and Richard Law. Sufficient conditions for the existence of the solution of this equation (the fixed point of the integral operator) were found. The question of uniqueness of the solution is also studied.

scholarly journals On Existence and Uniqueness of Solutions of a Nonlinear Integral Equation

2011 ◽  
Vol 2011 ◽  
pp. 1-7 ◽  
Author(s):  
M. Eshaghi Gordji ◽  
H. Baghani ◽  
O. Baghani
Keyword(s):  
Banach Space ◽  
Integral Equation ◽  
Fixed Point ◽  
Integral Operator ◽  
Existence And Uniqueness ◽  
Nonlinear Integral Equation ◽  
Uniqueness Of Solutions ◽  
Nonlinear Integral Operator

The purpose of this paper is to study the existence of fixed point for a nonlinear integral operator in the framework of Banach space . Later on, we give some examples of applications of this type of results.

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 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.

On existence result of a class of nonlinear integral equation

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3593-3597
Author(s):  
Ravindra Bisht
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Existence And Uniqueness ◽  
Existence Result ◽  
Nonlinear Integral Equation ◽  
Continuous Functions ◽  
Concave Functions ◽  
Real Numbers ◽  
Fixed Point Techniques ◽  
Uniqueness Of A Solution

Combining the approaches of functionals associated with h-concave functions and fixed point techniques, we study the existence and uniqueness of a solution for a class of nonlinear integral equation: x(t) = g1(t)-g2(t) + ? ?t,0 V1(t,s)h1(s,x(s))ds + ? ?T,0 V2(t,s)h2(s,x(s))ds; where C([0,T];R) denotes the space of all continuous functions on [0,T] equipped with the uniform metric and t?[0,T], ?,? are real numbers, g1, g2 ? C([0, T],R) and V1(t,s), V2(t,s), h1(t,s), h2(t,s) are continuous real-valued functions in [0,T]xR.

scholarly journals Existence and Uniqueness of the Solution for an Integral Equation with Supremum, via w-Distances

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1554 ◽  
Author(s):  
Veronica Ilea ◽  
Diana Otrocol
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Existence And Uniqueness ◽  
Stability Result ◽  
Fixed Point Problem ◽  
Comparison Theorems ◽  
Point Problem ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Uniqueness Of The Solution

Following the idea of T. Wongyat and W. Sintunavarat, we obtain some existence and uniqueness results for the solution of an integral equation with supremum. The paper ends with the study of Gronwall-type theorems, comparison theorems and a result regarding a Ulam–Hyers stability result for the corresponding fixed point problem.

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 Coupled fixed point theorems for new contractive mixed monotone mappings and applications to integral equations

Filomat ◽  
2014 ◽  
Vol 28 (6) ◽  
pp. 1253-1264 ◽  
Author(s):  
Hüseyin Işik ◽  
Duran Türkoğlu
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Nonlinear Integral Equation ◽  
Complete Metric Space ◽  
Coupled Fixed Point ◽  
Nonlinear Problems ◽  
Monotone Mappings ◽  
Mixed Monotone Property

The aim of this paper is to extend the results of Bhaskar and Lakshmikantham and some other authors and to prove some new coupled fixed point theorems for mappings having a mixed monotone property in a complete metric space endowed with a partial order. Our theorems can be used to investigate a large class of nonlinear problems. As an application, we discuss the existence and uniqueness for a solution of a nonlinear integral equation.

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 AN EXTENSION OF THE PRODUCT INTEGRATION METHOD TO L1 WITH APPLICATIONS IN ASTROPHYSICS

2016 ◽  
Vol 21 (6) ◽  
pp. 774-793 ◽  
Author(s):  
Laurence Grammont ◽  
Mario Ahues ◽  
Hanane Kaboul
Keyword(s):  
Integral Equation ◽  
Existence And Uniqueness ◽  
Integration Method ◽  
Sufficient Conditions ◽  
Iterative Refinement ◽  
Weakly Singular Kernel ◽  
Product Integration ◽  
Weakly Singular ◽  
Uniqueness Of The Solution ◽  
Product Integration Method

A Fredholm integral equation of the second kind in L1([a, b], C) with a weakly singular kernel is considered. Sufficient conditions are given for the existence and uniqueness of the solution. We adapt the product integration method proposed in C0 ([a, b], C) to apply it in L1 ([a, b], C), and discretize the equation. To improve the accuracy of the approximate solution, we use different iterative refinement schemes which we compare one to each other. Numerical evidence is given with an application in Astrophysics.

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.

Sign in / Sign up

Export Citation Format

Share Document