scholarly journals Existence, Uniqueness, and Approximation for Solutions of a Functional-integral Equation in Lp Spaces

2019 ◽  
Vol 20 (3) ◽  
pp. 403
Author(s):  
Suzete M Afonso ◽  
Juarez S Azevedo ◽  
Mariana P. G. Da Silva ◽  
Adson M Rocha
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Existence And Uniqueness ◽  
Functional Integral ◽  
Successive Approximation Method ◽  
Banach Fixed Point Theorem ◽  
Numerical Examples ◽  
Lp Spaces ◽  
Chebyshev Quadrature

In this work we consider the general functional-integral equation: \begin{equation*}y(t) = f\left(t, \int_{a}^{b} k(t,s)g(s,y(s))ds\right), \qquad t\in [a,b],\end{equation*}and give conditions that guarantee existence and uniqueness of solution in $L^p([a,b])$, with {$1<p<\infty$}.We use  Banach Fixed Point Theorem and employ the successive approximation method and Chebyshev quadrature for approximating the values of integrals. Finally, to illustrate the results of this work, we provide some numerical examples.

scholarly journals On Existence and Uniqueness of an Integrable Solution for a Fractional Volterra Integral Equation on 𝑹+

2020 ◽  
pp. 122-125
Author(s):  
Faez N. Ghaffoori
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Uniqueness Theorem ◽  
Point Theorem ◽  
Volterra Integral Equation ◽  
Existence And Uniqueness ◽  
Banach Fixed Point Theorem ◽  
Existence And Uniqueness Theorem ◽  
Integrable Solution

In this paper, by using the Banach fixed point theorem, we prove the existence and uniqueness theorem of a fractional Volterra integral equation in the space of Lebesgue integrable 𝐿1(𝑅+) on unbounded interval [0,∞).

scholarly journals Integrable Solutions of a Nonlinear Integral Equation via Noncompactness Measure and Krasnoselskii's Fixed Point Theorem

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Mahmoud Bousselsal ◽  
Sidi Hamidou Jah
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Functional Integral ◽  
Nonlinear Integral Equations ◽  
Measure Of Weak Noncompactness ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Noncompactness Measure

We study the existence of solutions of a nonlinear Volterra integral equation in the space L1[0,+∞). With the help of Krasnoselskii’s fixed point theorem and the theory of measure of weak noncompactness, we prove an existence result for a functional integral equation which includes several classes on nonlinear integral equations. Our results extend and generalize some previous works. An example is given to support our results.

scholarly journals The analysis of some special results of a Lasota–Wazewska model with mixed variable delays

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Ramazan Yazgan ◽  
Osman Tunç
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Existence And Uniqueness ◽  
Banach Fixed Point Theorem ◽  
Time Varying ◽  
Differential Inequalities ◽  
Almost Periodic ◽  
Variable Delays ◽  
Pseudo Almost Periodic ◽  
Mixed Variable

AbstractThis study is about getting some conditions that guarantee the existence and uniqueness of the weighted pseudo almost periodic (WPAP) solutions of a Lasota–Wazewska model with time-varying delays. Some adequate conditions have been obtained for the existence and uniqueness of the WPAP solutions of the Lasota–Wazewska model, which we dealt with using some differential inequalities, the WPAP theory, and the Banach fixed point theorem. Besides, an application is given to demonstrate the accuracy of the conditions of our main results.

scholarly journals The Existence and Uniqueness of Solutions for a Class of Nonlinear Fractional Differential Equations with Infinite Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Azizollah Babakhani ◽  
Dumitru Baleanu ◽  
Ravi P. Agarwal
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Fractional Derivatives ◽  
Infinite Delay ◽  
Banach Fixed Point Theorem ◽  
Uniqueness Of Solutions ◽  
Fractional Differential

We prove the existence and uniqueness of solutions for two classes of infinite delay nonlinear fractional order differential equations involving Riemann-Liouville fractional derivatives. The analysis is based on the alternative of the Leray-Schauder fixed-point theorem, the Banach fixed-point theorem, and the Arzela-Ascoli theorem inΩ={y:(−∞,b]→ℝ:y|(−∞,0]∈ℬ}such thaty|[0,b]is continuous andℬis a phase space.

scholarly journals Nonlinear Volterra Integral Equation of the Second Kind and Biorthogonal Systems

2010 ◽  
Vol 2010 ◽  
pp. 1-11 ◽  
Author(s):  
M. I. Berenguer ◽  
D. Gámez ◽  
A. I. Garralda-Guillem ◽  
M. C. Serrano Pérez
Keyword(s):  
Banach Space ◽  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Volterra Integral Equation ◽  
Biorthogonal System ◽  
Banach Fixed Point Theorem ◽  
Nonlinear Volterra Integral Equation ◽  
Numerical Resolution

We obtain an approximation of the solution of the nonlinear Volterra integral equation of the second kind, by means of a new method for its numerical resolution. The main tools used to establish it are the properties of a biorthogonal system in a Banach space and the Banach fixed point theorem.

scholarly journals BANACH FIXED POINT THEOREM ON ORTHOGONAL CONE METRIC SPACES

2021 ◽  
pp. 1239
Author(s):  
Zeinab Eivazi Damirchi Darsi Olia ◽  
Madjid Eshaghi Gordji ◽  
Davood Ebrahimi Bagha
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Uniqueness Of Solution ◽  
Banach Fixed Point Theorem ◽  
Cone Metric Spaces ◽  
Cone Metric

In this paper, we introduce new concept of orthogonal cone metric spaces. We stablish new versions of fixed point theorems in incomplete orthogonal cone metric spaces. As an application, we show the existence and uniqueness of solution of the periodic boundry value problem.

scholarly journals MITTAG-LEFFLER STABILITY ANALYSIS OF TEMPERED FRACTIONAL NEURAL NETWORKS WITH SHORT MEMORY AND VARIABLE-ORDER

Fractals ◽  
2021 ◽  
pp. 2140029
Author(s):  
CHUAN-YUN GU ◽  
FENG-XIA ZHENG ◽  
BABAK SHIRI
Keyword(s):  
Neural Networks ◽  
Fixed Point ◽  
Stability Analysis ◽  
Fixed Point Theorem ◽  
Banach Fixed Point Theorem ◽  
Stability Conditions ◽  
Variable Order ◽  
Numerical Examples ◽  
Short Memory ◽  
Theoretical Results

A class of tempered fractional neural networks is proposed in this paper. Stability conditions for tempered fractional neural networks are provided by using Banach fixed point theorem. Attractivity and Mittag-Leffler stability are given. In order to show the efficiency and convenience of the method used, tempered fractional neural networks with and without delay are discussed, respectively. Furthermore, short memory and variable-order tempered fractional neural networks are proposed under the global conditions. Finally, two numerical examples are used to demonstrate the theoretical results.

On a class of nonlinear Volterra-Fredholm q-integral equations

2014 ◽  
Vol 17 (1) ◽  
Author(s):  
Zeinab Mansour
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Fredholm Integral Equations ◽  
Banach Fixed Point Theorem ◽  
Continuous Solutions ◽  
Projective Metric ◽  
Uniqueness Criteria

AbstractIn this paper we investigate the existence and uniqueness of positive continuous solutions for a q-analogue of Volterra and Fredholm integral equations of first and second kinds. We derive the results by using three fixed point theorems introduced by Bushell in [7, 8]. Bushell derived his theorems by using the Cayley-Hilbert projective metric and Banach fixed point theorem. We also include some uniqueness criteria for the solutions of certain nonlinear q-integral equations provided that the solution exists in certain function spaces.

scholarly journals Existence and Asymptotic Stability of Solutions of a Functional Integral Equation via a Consequence of Sadovskii’s Theorem

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Agnieszka Chlebowicz ◽  
Mohamed Abdalla Darwish ◽  
Kishin Sadarangani
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Asymptotic Stability ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Functional Integral ◽  
Stability Of Solutions ◽  
Measures Of Noncompactness

Using the technique of measures of noncompactness and, in particular, a consequence of Sadovskii’s fixed point theorem, we prove a theorem about the existence and asymptotic stability of solutions of a functional integral equation. Moreover, in order to illustrate our results, we include one example and compare our results with those obtained in other papers appearing in the literature.

scholarly journals A NONLINEAR F-CONTRACTION FORM OF SADOVSKII'S FIXED POINT THEOREM AND ITS APPLICATION TO A FUNCTIONAL INTEGRAL EQUATION OF VOLTERRA TYPE

2021 ◽  
pp. 321
Author(s):  
Kourosh Nourouzi ◽  
Faezeh Zahedi ◽  
Donal O'Regan
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Functional Integral ◽  
Volterra Type

In this paper, we give a nonlinear F-contraction form of the Sadovskii fixedpoint theorem and we also investigate the existence of solutions for a functional integral equation of Volterra type.

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