Nonlinear Functional Integral Equations Research Articles

Existence of solutions for a class of system of functional integral equation via measure of noncompactness

In this paper, we give some generalization of Darbo’s fixed point theorem related to the measure of noncompactness, and present some results on the existence of coupled fixed point theorem for a special class of operators in a Banach space. Our results generalize and extend some comparable results in the literature. Also as an application, we study the existence of solution for a class of the system of nonlinear functional integral equations. Finally an example illustrating the mentioned applicability is also included.

Solvability of Functional Integral Equations in the Fréchet Space $${C(\Omega)}$$ C ( Ω )

This work deals with the existence of solutions for a class of nonlinear functional integral equations of Volterra type in the Frechet space of continuous functions on an unbounded subset \({\Omega}\) of \({\mathbb{R}^n}\). The equation was considered by Arab et al. (J Math 13(3):1197–1210, 2015). By choosing a different functional space and a different fixed point theorem in conjunction with some measures of noncompactness, we show that existence of continuous solutions can be proved under weaker conditions.

Asymptotic stability of solutions for a class of nonlinear functional integral equations of fractional order

In this paper, using a Darbo type fixed point theorem associated with the measure of noncompactness we prove a theorem on the existence of asymptotically stable solutions of some nonlinear functional integral equations in the space of continuous and bounded functions on R+ = [0,∞). We also give some examples satisfying the conditions our existence theorem.

The solvability of some nonlinear functional integral equations

In this paper, using a Darbo type fixed point theorem associated with the measure of noncompactness we prove a theorem on the existence of solutions of some nonlinear functional integral equations in the space of continuous functions on interval [0, a]. We give also some examples which show that the obtained results are applicable

A continuum of solutions in a Fréchet space of a nonlinear functional integral equation in N variables

In this paper, we investigate the set of solutions of a nonlinear functional integral equation in N variables in a Fréchet space. Applying a fixed point theorem of Krasnosel'skii type and a structure theorem of Krasnosel'skii and Perov, a sufficient condition is established such that the set of solutions is a continuum, that is, nonempty, compact and connected. Furthermore, based on Aronszajn type results and a theorem proved by Vidossich, we show that this solutions set is also a compact . This is also true with solutions set of a nonlinear Volterra–Hammerstein integral equation.

Some generalizations of a hybrid fixed point theorem in partially ordered metric spaces and nonlinear functional integral equations

Some generalizations of a hybrid fixed point theorem in partially ordered metric spaces and nonlinear functional integral equations

An existence result for a class of nonlinear functional integral equations

We consider a general nonlinear functional integral equation, and we prove the existence of solutions of this equation in the space of Lebesgue integrable functions on $\R^+$. Our analysis uses a recent version of Krasnosel'skii's fixed point theorem (Theorem \ref{2t1}) and the concept of the measure of weak noncompactness. In the appendix, we give an extension of Theorem~\ref{2t1} to expansive mappings.

Solvability of a general nonlinear integral equation in $L^1$ spaces by means of a measure of weak noncompactness

This paper is concerned with existence results for a quite general nonlinear functional integral equation in $L^1$ spaces. For this purpose, making use of the De Blasi measure of weak noncompactness, we first establish a new fixed point theorem of the nonautonomous superposition operators. After that, our theorem is applied to prove the solvability of the mentioned nonlinear functional integral equation.

On local attractivity of nonlinear functional integral equations via measures of noncompactness

In this paper, we prove the local attractivity of solutions for a certain nonlinear Volterra type functional integral equations. We rely on a measure theoretic fixed point theorem of Dhage (2008) for nonlinear D-set-contraction in Banach spaces. Finally, we furnish an example to validate all the hypotheses of our main result and to ensure the existence and ultimate attractivity of solutions for a numerical nonlinear functional integral equation.

Existence of solutions of functional integral equations of convolution type using a new construction of a measure of noncompactness on [formula omitted

Let Lp(R+) denote the space of Lebesgue integrable functions on R+ with the standard norm∥x∥p=(∫0∞|x(t)|pdt)1p.First, we define a new measure of noncompactness on the spaces Lp(R+) (1 ≤ p < ∞). In addition, we study the existence of entire solutions for a class of nonlinear functional integral equations of convolution type using Darbo’s fixed point theorem, which is associated with the new measure of noncompactness. We provide some examples to demonstrate that our results are applicable whereas the previous results are not.

Asymptotically Stable Solutions for a Nonlinear Functional Integral Equation

In this paper, the solvability and the existence of asymptotically stable solutions for a nonlinear functional integral equation are studied. The main tools are a fixed point theorem of Krasnosel’skii type, the dominated convergence theorem, and other results from functional analysis. In order to illustrate the result obtained here, an example is given.

Construction of a Measure of Noncompactness on $${BC(\Omega)}$$ B C ( Ω ) and its Application to Volterra Integral Equations

In the present paper, we investigate the construction of compact sets of bounded continuous functions on unbounded set \({\Omega}\) of \({\mathbb{R}^n}\), and then introduce a measure of noncompactness on this space. As an application, we study the existence of solutions for a class of nonlinear functional integral equations of Volterra type by using some fixed point theorems associated with this new measure of noncompactness. Obtained results generalize numerous other ones. We will also include some examples which show that our results are applicable where the previous ones are not.

An Application of Krasnoselskii Fixed Point Theorem to Some Nonlinear Functional Integral Equations

The purpose of this paper is to study the existence of solutions of some nonlinear functional integral equations in the space of continuous functions defined on interval under some conditions. To do this, we will use Krasnoselskii Fixed Point Theorem and Ascoli-Arzela Theorem. Finally we will give an example to illustrate our result.

Krasnoselskii Sabit Nokta Teoreminin Lineer Olmayan Bazı Fonksiyonel İntegral Denklemlere Uygulaması

The purpose of this paper is to study the existence of solutions of some nonlinear functional integral equations in the space of continuous functions defined on interval under some conditions. To do this, we will use Krasnoselskii Fixed Point Theorem and Ascoli-Arzela Theorem. Finally we will give an example to illustrate our result.

Nonlinear D-set contraction mappings in partially ordered normed linear spaces and applications to functional hybrid integral equations

In this paper the author introduces the notion of partially nonlinear D-set-contraction mappings in a partially ordered normed linear space and prove some hybrid fixed point theorems under certain mixed conditions from algebra, analysis and topology. The applications of abstract results presented here are given to perturbed nonlinear hybrid functional integral equations for proving the existence as well as global attractivity of the comparable solutions under certain monotonic conditions. The abstract theory developed in this paper is also useful to develop the algorithms for the solutions of some nonlinear problems of analysis and allied areas of mathematics.

A generalization of Darbo's fixed point theorem and local attractivity of generalized nonlinear functional integral equations

A generalization of Darbo's fixed point theorem and local attractivity of generalized nonlinear functional integral equations

On the solutions of a class of nonlinear functional integral equations in space C [0,a

On the solutions of a class of nonlinear functional integral equations in space C [0,a

On a generalized coupled fixed point theorem in C[0, 1] and its application to a class of coupled systems of functional-integral equations

In this paper, we present a result about the existence of a generalized coupled fixed point in the space C[0, 1]. Moreover, as an application of the result, we study the problem of existence and uniqueness of solution in C[0, 1] for a general system of nonlinear functional-integral equations with maximum.

Partially condensing mappings in partially ordered normed linar spaces and applications to functional integral equations

In this paper, the author introduces a notion of partially condensing mappings in a partially ordered normed linear space and proves some hybrid fixed point theorems under certain mixed conditions of algebra, analysis and topology. The applications of abstract results presented here are given to some nonlinear functional integral equations for proving the existence as well as global attractivity of the comparable solutions under certain monotonicity conditions. The abstract theory presented here is very much useful to develop the algorithms for the solutions of some nonlinear problems of analysis and allied areas of mathematics. A realization of of our hypotheses is also indicated by a numerical example.

A fixed point theorem for nonautonomous type superposition operators and integrable solutions of a general nonlinear functional integral equation

We first establish a new fixed point theorem for nonautonomous type superposition operators. After that, we prove the existence of integrable solutions for a general nonlinear functional integral equation in an space on an unbounded interval by using our theorem. Our main tool is the measure of weak noncompactness. MSC:47H30, 47H08.