Generalization Of Darbo Research Articles

On some generalizations of Darbo- and Sadovskii- type fixed point theorems in Fréchet spaces

Integral equations form an essential part of nonlinear analysis. In many situations, when seeking solutions to such equations, we utilize fixed-point theorems. Among the most well-known and useful in this regard are the theorems of Darbo and Sadovskii, which generalize the classical results of Schauder and Tikhonov. These theorems have seen many generalizations. The aim of the paper is to strengthen (by weakening the assumptions) several known Darbo- and Sadovskii-type fixed-point theorems in the so-called power version for Fréchet spaces, which are particularly useful for studying the solvability of equations defined on an unbounded interval. A theorem on the existence of solutions to a nonlinear integral equation, illustrating the application of our main result, is also provided.

Nonlocal problems for retarted fractional differential equations via generalization of Darbo’s fixed point theorem

Nonlocal problems for retarted fractional differential equations via generalization of Darbo’s fixed point theorem

Existence of a solution to an infinite system of weighted fractional integral equations of a function with respect to another function via a measure of noncompactness

Abstract In this article, some new generalizations of Darbo’s fixed-point theorem are given and the solvability of an infinite system of weighted fractional integral equations of a function with respect to another function is studied. Also, with the help of a proper example, we illustrate our findings.

On Solutions of Hybrid–Sturm-Liouville–Langevin Equations with Generalized Versions of Caputo Fractional Derivatives

The main intention of this research article is to introduce a new class of generalized fractional differential equations that fall into the categories of Sturm-Liouville’s, Langevin’s, and hybrid’s problems involving Y -Caputo fractional derivatives. The existence of the solutions of the proposed equations is discussed by using the technique of the measure of noncompactness related to the fixed point theorem, which is a generalization of Darbo’s fixed point theorem. Additionally, pertinent examples are provided along with the different values of the function Y to confirm the validity of the reported results.

Extension of Darbo’s fixed point theorem via shifting distance functions and its application

In this paper, we discuss solvability of infinite system of fractional integral equations (FIE) of mixed type. To achieve this goal, we first use shifting distance function to establish a new generalization of Darbo’s fixed point theorem, and then apply it to the FIEs to establish the existence of solution on tempered sequence space. Finally, we verify our results by considering a suitable example.

Simulation functions and Meir–Keeler condensing operators with application to integral equations

We propose a new concept of condensing operators by using a notion of measure of non-compactness in the setting of Banach spaces and establish a new generalization of Darbo’s fixed point theorem. We also show the applicability of our results to integral equations. A concrete example will be presented to support the application part.

A generalization of Darbo's theorem with application to the solvability of systems of integral-differential equations in Sobolev spaces

‎In this article‎, ‎we introduce the notion of $(alpha,beta)$-generalized Meir-Keeler condensing operator in a‎ ‎Banach space‎, ‎a characterization using strictly L-functions and provide an extension of Darbo's fixed point theorem associated with measures‎ of noncompactness‎. ‎Then‎, ‎we establish some results on the existence of coupled fixed points for a‎ ‎class of condensing operators in Banach spaces‎. ‎As an application‎, ‎we study the‎ ‎problem of existence of entire solutions for a general system of nonlinear integral-differential equations in a Sobolev space‎. ‎Further‎, an example is presented to verify the effectiveness and applicability of our main results‎.

Nonlocal Fractional Hybrid Boundary Value Problems Involving Mixed Fractional Derivatives and Integrals via a Generalization of Darbo’s Theorem

In this work, a new existence result is established for a nonlocal hybrid boundary value problem which contains one left Caputo and one right Riemann–Liouville fractional derivatives and integrals. The main result is proved by applying a new generalization of Darbo’s theorem associated with measures of noncompactness. Finally, an example to justify the theoretical result is also presented.

Nonlocal coupled hybrid fractional system of mixed fractional derivatives via an extension of Darbo's theorem

<abstract> In this work a new existence result is established for a coupled fractional system consisting of one Caputo and one Riemann-Liouville fractional derivatives and nonlocal hybrid boundary conditions. A new generalization of Darbo's theorem associated with measures of noncompactness is the main tool in our approach. An example is constructed to justify the theoretical result. </abstract>

A generalization of Darbo's fixed point theorem with an application to fractional integral equations

A generalization of Darbo's fixed point theorem with an application to fractional integral equations

The Technique of Quadruple Fixed Points for Solving Functional Integral Equations under a Measure of Noncompactness

Under the idea of a measure of noncompactness, some fixed point results are proposed and a generalization of Darbo’s fixed point theorem is given in this manuscript. Furthermore, some novel quadruple fixed points results via a measure of noncompactness for a general class of functions are presented. Ultimately, the solutions to a system of non-linear functional integral equations by the fixed point results obtained are discussed, and non-trivial examples to illustrate the validity of our study are derived.

A New Common Fixed Point Theorem for Three Commuting Mappings

In the present paper, we propose a common fixed point theorem for three commuting mappings via a new contractive condition which generalizes fixed point theorems of Darbo, Hajji and Aghajani et al. An application is also given to illustrate our main result. Moreover, several consequences are derived, which are generalizations of Darbo’s fixed point theorem and a Hajji’s result.

New Generalization of Darbo's Fixed Point Theorem via $alpha$-admissible Simulation Functions with Application

In this paper, at first, we introduce $alpha_{mu}$-admissible, $Z_mu$-contraction and $N_{mu}$-contraction via simulation functions. We prove some new fixed point theorems for defined class of contractions via $alpha$-admissible simulation mappings, as well. Our results can be viewed as extension of the corresponding results in this area. Moreover, some examples and an application to functional integral equations are given to support the obtained results.

Existence of Solutions for a System of Integral Equations Using a Generalization of Darbo’s Fixed Point Theorem

In this paper, an extension of Darbo’s fixed point theorem via θ -F-contractions in a Banach space has been presented. Measure of noncompactness approach is the main tool in the presentation of our proofs. As an application, we study the existence of solutions for a system of integral equations. Finally, we present a concrete example to support the effectiveness of our results.

Solutions of an infinite system of integral equations of Volterra-Stieltjes type in the sequence spaces $\ell_{p} (1&lt;p&lt;\infty)$ 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.

Existence of Solution for Non-Linear Functional Integral Equations of Two Variables in Banach Algebra

The aim of this article is to establish the existence of the solution of non-linear functional integral equations x ( l , h ) = U ( l , h , x ( l , h ) ) + F l , h , ∫ 0 l ∫ 0 h P ( l , h , r , u , x ( r , u ) ) d r d u , x ( l , h ) × G l , h , ∫ 0 a ∫ 0 a Q l , h , r , u , x ( r , u ) d r d u , x ( l , h ) of two variables, which is of the form of two operators in the setting of Banach algebra C [ 0 , a ] × [ 0 , a ] , a &gt; 0 . Our methodology relies upon the measure of noncompactness related to the fixed point hypothesis. We have used the measure of noncompactness on C [ 0 , a ] × [ 0 , a ] and a fixed point theorem, which is a generalization of Darbo’s fixed point theorem for the product of operators. We additionally illustrate our outcome with the help of an interesting example.

Positive Solution of a Quadratic Integral Equation Using Generalization of Darbo’s Fixed Point Theorem

The objective of this article is to establish a fixed point theorem using different class of control functions, which is a generalization of Darbo’s fixed point theorem (DFPT) and its various versions obtained by several authors. Using this result we obtain existence of at least one positive solution for a quadratic integral equation of Fredholm type.

Some New Generalization of Darbo’s Fixed Point Theorem and Its Application on Integral Equations

In this article, we propose some new fixed point theorem involving measure of noncompactness and control function. Further, we prove the existence of a solution of functional integral equations in two variables by using this fixed point theorem in Banach Algebra, and also illustrate the results with the help of an example.

Application of measures of noncompactness to the system of integral equations

AbstractIn this paper, by applying a measure of noncompactness in the space L∞(ℝn) and a new generalization of Darbo fixed point theorem, we study the existence of solutions for a class of the syst...

Generalizations of Darbo’s fixed point theorem and solvability of integral and differential systems

In this paper, we establish some new generalizations of Darbo’s fixed point theorem for multivalued mappings. Moreover, we prove the existence of solutions for a class of integral equations by Darbo’s fixed point theorem and the existence of solutions for a class of differential inclusions using a generalization of Darbo’s fixed point theorem.