Infinite System Of Integral Equations Research Articles

On the existence of solutions for an infinite system of integral equations

On the existence of solutions for an infinite system of integral equations

A New Survey of Measures of Noncompactness and Their Applications

We present a survey of the theory of measures of noncompactness and discuss some fixed point theorems of Darbo’s type. We apply the technique of measures of noncompactness to the characterization of classes of compact operators between certain sequence spaces, in solving infinite systems of integral equations in some sequence spaces. We also present some recent results related to the existence of best proximity points (pairs) for some classes of cyclic and noncyclic condensing operators in Banach spaces equipped with a suitable measure of noncompactness. Finally, we discuss the existence of an optimal solution for systems of integro–differentials.

The Study of the Solvability of Infinite Systems of Integral Equations via Measures of Noncompactness

The paper is devoted to investigate the existence of solutions of infinite systems of nonlinear quadratic integral equations of Volterra type. We look for solutions of those infinite systems of integral equations which are defined, continuous and bounded on the real half-axis and take real values. In our considerations the basic role will be played by the technique of measures of noncompactness defined in the space of functions defined, continuous and bounded on the real half-axis with values in the sequence space consisting of real sequences equipped with the standard supremum norm. We are going to prove an existence result which generalizes all recently obtained results for infinite systems of integral equations. An example illustrating the obtained result will be included.

Some Coincidence and Common Fixed-Point Results on Cone b 2 -Metric Spaces over Banach Algebras with Applications to the Infinite System of Integral Equations

In this article, common fixed-point theorems for self-mappings under different types of generalized contractions in the context of the cone b 2 -metric space over the Banach algebra are discussed. The existence results obtained strengthen the ones mentioned previously in the literature. An example and an application to the infinite system of integral equations are also presented to validate the main results.

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

"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."

Existence of solutions to infinite systems of nonlinear integral equations on the real half-axis

In this article we study the solvability of an infinite system of integral equations of Volterra-Hammerstein type in the space of functions defined, continuous and oundedon the real half-axis with values in the sequence space \(l_1\). We extend a known existence result for such an infinite system of integral equations and prove a theorem applicable to a wider class of considered infinite systems. We also give an example to show the usefulness of our result.
 For more information see https://ejde.math.txstate.edu/Volumes/2021/61/abstr.html

On solvability of infinite system of integral equations of Volterra together with Hammerstein type in the Fréchet spaces

In this paper, we prove some fixed point theorems associated with Tychonoff fixed point theorem and measure of noncompactness in the Fr?chet spaces. Moreover, as an application of our results, we analyze the existence of solutions for infinite system of integral equations of Volterra together with Hammerstein type. Finally, we present an example to illustrate the effectiveness of our results.

Fixed-Point Results for Generalized α -Admissible Hardy-Rogers’ Contractions in Cone b 2 -Metric Spaces over Banach’s Algebras with Application

In the current manuscript, the notion of a cone b 2 -metric space over Banach’s algebra with parameter b ≻ ¯ e is introduced. Furthermore, using α -admissible Hardy-Rogers’ contractive conditions, we have proven fixed-point theorems for self-mappings, which generalize and strengthen many of the conclusions in existing literature. In order to verify our key result, a nontrivial example is given, and as an application, we proved a theorem that shows the existence of a solution of an infinite system of integral equations.

Solvability of an infinite system of integral equations on the real half-axis

Abstract The aim of the paper is to investigate the solvability of an infinite system of nonlinear integral equations on the real half-axis. The considerations will be located in the space of function sequences which are bounded at every point of the half-axis. The main tool used in the investigations is the technique associated with measures of noncompactness in the space of functions defined, continuous and bounded on the real half-axis with values in the space l ∞ consisting of real bounded sequences endowed with the standard supremum norm. The essential role in our considerations is played by the fact that we will use a measure of noncompactness constructed on the basis of a measure of noncompactness in the mentioned sequence space l ∞. An example illustrating our result will be included.

Existence of solutions for the infinite systems of integral equations in the space L∞(∂n)

In this paper, by applying the behavior of measure of noncompactness in L∞(Rn), we study the existence of solutions of an infinite system of integral equations in the space L∞(Rn). Finally, an example is included to show the usefulness of the outcome.

An extension of Tychonoff fixed point theorem with application to the solvability of the infinite systems of integral equations in the Fréchet spaces

An extension of Tychonoff fixed point theorem with application to the solvability of the infinite systems of integral equations in the Fréchet spaces

Solutions of an infinite system of integral equations of Volterra-Stieltjes type in the sequence spaces $\ell_{p} (1<p<\infty)$ and $c_{0}$

In this paper, by applying the technique of measure of noncompactness and a new generalization of Darbo's theorem, we study the existence of solutions for an infinite system of integral equations in two variables. The obtained results extend and generalize some related results in previous work. Finally, some examples are included to ascertain the usefulness of the outcome.

Solvability of an infinite system of nonlinear integral equations of Volterra-Hammerstein type

AbstractThe purpose of the paper is to study the solvability of an infinite system of integral equations of Volterra-Hammerstein type on an unbounded interval. We show that such a system of integral equations has at least one solution in the space of functions defined, continuous and bounded on the real half-axis with values in the spacel1consisting of all real sequences whose series is absolutely convergent. To prove this result we construct a suitable measure of noncompactness in the mentioned function space and we use that measure together with a fixed point theorem of Darbo type.

On solutions of an infinite system of nonlinear integral equations on the real half-axis

We investigate the existence of solutions of an infinite system of integral equations of Volterra–Hammerstein type on the real half-axis. The method applied in our study is connected with the construction of a suitable measure of noncompactness in the space of continuous and bounded functions defined on the real half-axis with values in the space c0 consisting of real sequences converging to zero and equipped with the classical supremum norm. We use the mentioned measure of noncompactness together with a fixed point theorem of Darbo type. Our investigations are illustrated by an example.

Infinite system of integral equations in two variables of hammerstein type in C0 and ℓ1 spaces

The principal aim of this paper is to study the solvability of infinite system of integral equations in two variables of Hammerstein type in the Banach spaces C0 and ?1 using Meir-Keeler condensing operators and measure of noncompactness. In this study we give some examples.

Infinite systems of integral equations in Fr\'{e}chet spaces using the notion of L-functions

Infinite systems of integral equations in Fr\'{e}chet spaces using the notion of L-functions

Application of measure of noncompactness for solvability of the infinite system of integral equations in two variables in $$\ell _{p}\left( 1<p< \infty \right) $$ ℓ p 1 < p < ∞

In this article, we establish the existence of solution of infinite systems of integral equations in two variables in the sequence space $$\ell _{p}(1<p<\infty )$$ by using Meir–Keeler condensing operators. We explain the results with the help of simple examples.

Solvability of the infinite system of integral equations in two variables in the sequence spacesc0andℓ1

In this article, we establish the existence of solution of infinite systems of integral equations in two variables in the sequence spaces c 0 and ℓ 1 by using Meir–Keeler condensing operators. We explain the results with the help of simple examples.

Existence of solutions of infinite systems of integral equations in the Frechet spaces

In this paper we apply the technique of measures of noncompactness to the theory of infinite system of integral equations in the Fr´echet spaces. Our aim is to provide a few generalization of Tychonoff fixed point theorem and prove the existence of solutions for infinite systems of nonlinear integral equations with help of the technique of measures of noncompactness and a generalization of Tychonoff fixed point theorem. Also, we present an example of nonlinear integral equations to show the efficiency of our results. Our results extend several comparable results obtained in the previous literature.

Existence of solutions of infinite systems of integral equations in two variables via measure of noncompactness

The aim of this paper is to establish fixed point theorems for condensing operators in the Fréchet spaces. In our considerations we apply the technique of measures of noncompactness in conjunction with the Tychonoff fixed point theorem. Moreover, as an application, we study the problem of the existence of solutions for infinite systems of integral equations in two variables. The results obtained extend several ones. Finally, an example is presented to show the efficiency of our results.