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 The Existence and Attractivity of Solutions of an Urysohn Integral Equation on an Unbounded Interval

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Mohamed Abdalla Darwish ◽  
Józef Banaś ◽  
Ebraheem O. Alzahrani
Keyword(s):  
Banach Space ◽  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Main Tool ◽  
Measures Of Noncompactness ◽  
Unbounded Interval ◽  
Real Functions ◽  
Half Axis

We prove a result on the existence and uniform attractivity of solutions of an Urysohn integral equation. Our considerations are conducted in the Banach space consisting of real functions which are bounded and continuous on the nonnegative real half axis. The main tool used in investigations is the technique associated with the measures of noncompactness and a fixed point theorem of Darbo type. An example showing the utility of the obtained results is also included.

scholarly journals On the existence of solutions for non-linear functional integral equation

Filomat ◽  
2010 ◽  
Vol 24 (4) ◽  
pp. 17-23
Author(s):  
E.M. El-Abd
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Linear Functional ◽  
Measure Of Noncompactness ◽  
Existence Of Solutions ◽  
Functional Integral ◽  
Nonlinear Functional ◽  
Darbo Fixed Point Theorem

We have proved the existence of monotonic solutions of a nonlinear functional integeral equation by using Darbo fixed point theorem associated with a measure of noncompactness.

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 Existence of solutions for hybrid fractional pantograph equations

2015 ◽  
Vol 9 (1) ◽  
pp. 150-167 ◽  
Author(s):  
Mohamed Darwish ◽  
Kishin Sadarangani
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fractional Derivative ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Banach Algebras ◽  
Type Condition ◽  
Measures Of Noncompactness ◽  
Pantograph Equation ◽  
Liouville Fractional Derivative

In this paper, we study the existence of the hybrid fractional pantograph equation {D?0+[x(t)/f(t,x(t),x(?t))= g(t,x(t), x(?t)), 0 < t < 1, x(0) = 0, where ?,?,? ?((0,1) and D?0+ denotes the Riemann-Liouville fractional derivative. The results are obtained using the technique of measures of noncompactness in the Banach algebras and a fixed point theorem for the product of two operators verifying a Darbo type condition. Some examples are provided to illustrate our results.

scholarly journals On fuzzy Volterra integral equations with deviating arguments

2004 ◽  
Vol 2004 (2) ◽  
pp. 169-176 ◽  
Author(s):  
K. Balachandran ◽  
P. Prakash
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Volterra Integral Equations ◽  
Deviating Arguments ◽  
Darbo Fixed Point Theorem

We investigate the problem of existence of solutions of fuzzy Volterra integral equations with deviating arguments. The results are obtained by using the Darbo fixed point theorem.

scholarly journals Existence of solutions of nonlinear differential equations with deviating arguments

1991 ◽  
Vol 44 (3) ◽  
pp. 467-476
Author(s):  
K. Balachandran ◽  
S. Ilamaran
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Existence Theorem ◽  
Point Theorem ◽  
Measure Of Noncompactness ◽  
Existence Of Solutions ◽  
Nonlinear Differential Equations ◽  
Deviating Arguments ◽  
Darbo Fixed Point Theorem

We prove an existence theorem for nonlinear differential equations with deviating arguments and with implicit derivatives. The proof is based on the notion of measure of noncompactness and the Darbo fixed point theorem.

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.

MEASURES OF NONCOMPACTNESS IN A SOBOLEV SPACE AND INTEGRO-DIFFERENTIAL EQUATIONS

2016 ◽  
Vol 94 (3) ◽  
pp. 497-506
Author(s):  
REZA ALLAHYARI ◽  
REZA ARAB ◽  
ALI SHOLE HAGHIGHI
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Sobolev Space ◽  
Differential Equations ◽  
Point Theorem ◽  
Measure Of Noncompactness ◽  
Existence Of Solutions ◽  
Measures Of Noncompactness ◽  
Darbo’S Fixed Point Theorem

The aim of this paper is to introduce a new measure of noncompactness on the Sobolev space$W^{n,p}[0,T]$. As an application, we investigate the existence of solutions for some classes of functional integro-differential equations in this space using Darbo’s fixed point theorem.

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.

Sign in / Sign up

Export Citation Format

Share Document