scholarly journals Existence and Characterization of Solutions of Nonlinear Volterra-Stieltjes Integral Equations in Two Variables

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Mohamed Abdalla Darwish ◽  
Józef Banaś
Keyword(s):  
Integral Equations ◽  
Nonlinear Integral Equation ◽  
Existence Of Solutions ◽  
Stieltjes Integral ◽  
Basic Tool ◽  
Measures Of Noncompactness ◽  
Characterization Of Solutions ◽  
Fractional Orders ◽  
Stieltjes Type

The paper is devoted mainly to the study of the existence of solutions depending on two variables of a nonlinear integral equation of Volterra-Stieltjes type. The basic tool used in investigations is the technique of measures of noncompactness and Darbo’s fixed point theorem. The results obtained in the paper are applicable, in a particular case, to the nonlinear partial integral equations of fractional orders.

scholarly journals The Technique of Measures of Noncompactness in Banach Algebras and Its Applications to Integral Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-15 ◽  
Author(s):  
Józef Banaś ◽  
Szymon Dudek
Keyword(s):  
Banach Algebra ◽  
Integral Equations ◽  
Banach Algebras ◽  
Functional Integral ◽  
Existence Results ◽  
Measures Of Noncompactness ◽  
Nonlinear Functional ◽  
Half Axis ◽  
Functional Integral Equations

We study the solvability of some nonlinear functional integral equations in the Banach algebra of real functions defined, continuous, and bounded on the real half axis. We apply the technique of measures of noncompactness in order to obtain existence results for equations in question. Additionally, that technique allows us to obtain some characterization of considered integral equations. An example illustrating the obtained results is also included.

scholarly journals A Unified Approach to Some Classes of Nonlinear Integral Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Nurgali K. Ashirbayev ◽  
Józef Banaś ◽  
Raina Bekmoldayeva
Keyword(s):  
Integral Equations ◽  
Stieltjes Integral ◽  
View Point ◽  
Unified Approach ◽  
Nonlinear Integral Equations ◽  
Several Variables ◽  
Quadratic Integral ◽  
Function Of Two Variables ◽  
Fractional Orders ◽  
Quadratic Integral Equations

We are going to discuss some important classes of nonlinear integral equations such as integral equations of Volterra-Chandrasekhar type, quadratic integral equations of fractional orders, nonlinear integral equations of Volterra-Wiener-Hopf type, and nonlinear integral equations of Erdélyi-Kober type. Those integral equations play very significant role in applications to the description of numerous real world events. Our aim is to show that the mentioned integral equations can be treated from the view point of nonlinear Volterra-Stieltjes integral equations. The Riemann-Stieltjes integral appearing in those integral equations is generated by a function of two variables. The choice of a suitable generating function enables us to obtain various kinds of integral equations. Some results concerning nonlinear Volterra-Stieltjes integral equations in several variables will be also discussed.

scholarly journals On Monotonic and Nonnegative Solutions of a Nonlinear Volterra-Stieltjes Integral Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Tomasz Zając
Keyword(s):  
Integral Equation ◽  
Integral Equations ◽  
Bounded Variation ◽  
Fractional Integral ◽  
Functions Of Bounded Variation ◽  
Stieltjes Integral ◽  
Measures Of Noncompactness ◽  
Bounded Interval ◽  
Nonnegative Solutions ◽  
Real Functions

We study the existence of monotonic and nonnegative solutions of a nonlinear quadratic Volterra-Stieltjes integral equation in the space of real functions being continuous on a bounded interval. The main tools used in our considerations are the technique of measures of noncompactness in connection with the theory of functions of bounded variation and the theory of Riemann-Stieltjes integral. The obtained results can be easily applied to the class of fractional integral equations and Volterra-Chandrasekhar integral equations, among others.

scholarly journals Boundary value problems of nonlinear fractional q-difference (integral) equations with two fractional orders and four-point nonlocal integral boundary conditions

Filomat ◽  
2014 ◽  
Vol 28 (8) ◽  
pp. 1719-1736 ◽  
Author(s):  
Bashir Ahmad ◽  
Juan Nieto ◽  
Ahmed Alsaedi ◽  
Hana Al-Hutami
Keyword(s):  
Boundary Conditions ◽  
Integral Equations ◽  
Existence Of Solutions ◽  
Fixed Point Theory ◽  
Integral Boundary Conditions ◽  
Point Theory ◽  
Existence Results ◽  
Integral Boundary ◽  
Nonlocal Integral Boundary Conditions ◽  
Fractional Orders

This paper investigates the existence of solutions for nonlinear fractional q-difference equations and q-difference integral equations involving two fractional orders with four-point nonlocal integral boundary conditions. The existence results are obtained by applying some traditional tools of fixed point theory, and are illustrated with examples.

scholarly journals Measures of noncompactness and infinite systems of integral equations of Urysohn type in $L^\infty(\mathfrak{G})$

2021 ◽  
Vol 37 (3) ◽  
pp. 407-416
Author(s):  
SHAHRAM BANAEI ◽  
◽  
VAHID PARVANEH ◽  
MOHAMMAD MURSALEEN ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Fixed Point Theorems ◽  
Measure Of Noncompactness ◽  
Existence Of Solutions ◽  
Fréchet Space ◽  
Measures Of Noncompactness ◽  
Infinite Systems ◽  
Type Integral ◽  
Systems Of Integral Equations

"In this article, applying the concept of measure of noncompactness, some fixed point theorems in the Fréchet space $L^\infty(\mathfrak{G})$ (where $\mathfrak{G}\subseteq \mathbb{R}^{\omega}$) have been proved. We handle our obtained consequences to inquiry the existence of solutions for infinite systems of Urysohn type integral equations. Our results extend some famous related results in the literature. Finally, to indicate the effectiveness of our results we present a genuine example."

scholarly journals On the solvability of some nonlinear functional integral equations on Lp(R+)

Filomat ◽  
2021 ◽  
Vol 35 (6) ◽  
pp. 1841-1850
Author(s):  
Mahmoud Bousselsal
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Measure Of Noncompactness ◽  
Existence Of Solutions ◽  
Functional Integral ◽  
Basic Tool ◽  
Nonlinear Functional ◽  
The Fixed Point Theorem ◽  
Functional Integral Equations

In this paper, we prove theorems on the existence of solutions in Lp(R+), 1 ? p < ?, for some functional integral equations. The basic tool used in the proof is the fixed point theorem due to Darbo with respect to so called measure of noncompactness. The obtained results generalize and extend several ones obtained earlier in many papers and monographs. An example which shows the applicability of our results is also included.

scholarly journals On the solvability of nonlinear integral equations in Lebesgue space

Filomat ◽  
2009 ◽  
Vol 23 (3) ◽  
pp. 203-209
Author(s):  
E.M. El-Abd
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Lebesgue Space ◽  
Nonlinear Integral Equation ◽  
Basic Tool ◽  
Nonlinear Integral Equations ◽  
Measure Of Weak Noncompactness ◽  
The Fixed Point Theorem

In this paper we prove theorems on the existence of integrable and monotonic solutions of nonlinear integral equation in Lebesgue Space. The basic tool used in the proof is the fixed point theorem due to Darbo with respect to the so-called measure of weak noncompactness.

scholarly journals Singular Lebesgue-Stieltjes integral equations

1941 ◽  
Vol 74 (0) ◽  
pp. 197-310 ◽  
Author(s):  
W. J. Trjitzinsky
Keyword(s):  
Integral Equations ◽  
Stieltjes Integral
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