scholarly journals Solvability of a Quadratic Integral Equation of Fredholm Type with Supremum in Hölder Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
J. Caballero Mena ◽  
R. Nalepa ◽  
K. Sadarangani
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Hölder Condition ◽  
Fredholm Type ◽  
Quadratic Integral Equation ◽  
Quadratic Integral ◽  
Holder Spaces

Using the classical Schauder fixed point theorem, we prove the existence of solutions of a quadratic integral equation of Fredholm type with supremum in the space of functions satisfying the Hölder condition.

scholarly journals On the Existence of the Solutions of a Fredholm Integral Equation with a Modified Argument in Hölder Spaces

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 522 ◽  
Author(s):  
Merve Temizer Ersoy ◽  
Hasan Furkan
Keyword(s):  
Integral Equation ◽  
Existence Of Solutions ◽  
Hölder Spaces ◽  
Fredholm Type ◽  
Relative Compactness ◽  
Quadratic Integral Equation ◽  
Quadratic Integral ◽  
Conclusion Section ◽  
The Given ◽  
Holder Spaces

This article concerns the entity of solutions of a quadratic integral equation of the Fredholm type with an altered argument, x ( t ) = p ( t ) + x ( t ) ∫ 0 1 k ( t , τ ) ( T x ) ( τ ) d τ , where p , k are given functions, T is the given operator satisfying conditions specified later and x is an unknown function. Through the classical Schauder fixed point theorem and a new conclusion about the relative compactness in Hölder spaces, we obtain the existence of solutions under certain assumptions. Our work is more general than the previous works in the Conclusion section. At the end, we introduce several tangible examples where our entity result can be adopted.

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 An Extension of Darbo’s Theorem and Its Application

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
A. Samadi ◽  
M. B. Ghaemi
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Measures Of Noncompactness ◽  
Darbo Fixed Point Theorem ◽  
Real Functions

Here, some extensions of Darbo fixed point theorem associated with measures of noncompactness are proved. Then, as an application, our attention is focused on the existence of solutions of the integral equationx(t)=F(t,f(t,x(α1(t)),  x(α2(t))),((Tx)(t)/Γ(α))×∫0t‍(u(t,s,max⁡[0,r(s)]⁡|x(γ1(τ))|,  max⁡[0,r(s)]⁡|x(γ2(τ))|)/(t-s)1-α)ds,  ∫0∞v(t,s,x(t))ds),    0<α≤1,t∈[0,1]in the space of real functions defined and continuous on the interval[0,1].

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.

scholarly journals Fixed points of $(\psi, \phi)-$contractions and Fredholm type integral equation

2021 ◽  
Vol 2 (1) ◽  
pp. 91-100
Author(s):  
Nabil Mlaiki ◽  
Doaa Rizk ◽  
Fatima Azmi
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Point Theorem ◽  
Metric Spaces ◽  
Fredholm Type ◽  
Contractive Mappings ◽  
Type Integral

In this paper, we establish a fixed point theorem for controlled rectangular $b-$metric spaces for mappings that satisfy $(\psi, \phi)-$contractive mappings. Also, we give an application of our results as an integral equation.

scholarly journals On the Space of Functions with Growths Tempered by a Modulus of Continuity and Its Applications

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Józef Banaś ◽  
Rafał Nalepa
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Modulus Of Continuity ◽  
Existence Result ◽  
Sufficient Condition ◽  
Hölder Condition ◽  
Fredholm Type ◽  
Relative Compactness ◽  
Quadratic Integral ◽  
Quadratic Integral Equations

We are going to study the space of real functions defined on a bounded metric space and having growths tempered by a modulus of continuity. We prove also a sufficient condition for the relative compactness in the mentioned function space. Using that condition and the classical Schauder fixed point theorem, we show the existence theorem for some quadratic integral equations of Fredholm type in the space of functions satisfying the Hölder condition. An example illustrating the mentioned existence result is also included.

scholarly journals Applications of a Fixed Point Result for Solving Nonlinear Fractional and Integral Differential Equations

2021 ◽  
Vol 5 (4) ◽  
pp. 211
Author(s):  
Liliana Guran ◽  
Zoran D. Mitrović ◽  
G. Sudhaamsh Mohan Reddy ◽  
Abdelkader Belhenniche ◽  
Stojan Radenović
Keyword(s):  
Differential Equation ◽  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Fractional Differential Equation ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Fractional Differential ◽  
Integral Differential Equations

In this article, we apply one fixed point theorem in the setting of b-metric-like spaces to prove the existence of solutions for one type of Caputo fractional differential equation as well as the existence of solutions for one integral equation created in mechanical engineering.

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