Measure Of Weak Noncompactness Research Articles

FIXED-POINT THEOREMS FOR MEIR–KEELER MULTIVALUED MAPS AND APPLICATION

This work is intended for a generalization of Darbo’s fixed-point theorem by using multivalued condensing operators, and a measure of weak noncompactness which does not necessarily possess the maximum property. Moreover, we prove some fixed-point theorems in Banach algebras which satisfy an appointed weak sequential condition. As an application, we establish the existence of solutions for a functional integral inclusion.

Solvability in weighted L1-spaces for the m-product of integral equations and model of the dynamics of the capillary rise

This article focuses on presenting a modified Hölder inequality and a new measure of noncompactness in L1N(R+) and applying them in proving two existence theorems (the existence and the uniqueness) of solutions for m-product of integral equations in the weighted Lebesgue spaces L1N(R+). This permits us to examine a model of the dynamics of the capillary rise of a fluid inside a tubular column in weighted Lebesgue spaces, which generalize the former results in the available literature. We utilize the analysis of fixed point hypothesis concerning a proper measure of weak noncompactness (MWNC) to get our outcomes. An example to validate our analysis is included.

A Measure of Weak Noncompactness in $$L^1({\mathbb {R}}^N)$$ and Applications

A Measure of Weak Noncompactness in $$L^1({\mathbb {R}}^N)$$ and Applications

Generalized form of fixed-point theorems in generalized Banach algebra relative to the weak topology with an application

In this paper, a general hybrid fixed point theorem for the contractive mappings in generalized Banach spaces is proved via measure of weak non-compactness and it is further applied to fractional integral equations for proving the existence results for the solutions under mixed Lipschitz and weakly sequentially continuous conditions. Finally, an example is given to illustrate the result.

Leray–Schauder Fixed Point Theorems for Block Operator Matrix with an Application

In this paper, we establish some new variants of Leray–Schauder-type fixed point theorems for a 2 × 2 block operator matrix defined on nonempty, closed, and convex subsets Ω of Banach spaces. Note here that Ω need not be bounded. These results are formulated in terms of weak sequential continuity and the technique of De Blasi measure of weak noncompactness on countably subsets. We will also prove the existence of solutions for a coupled system of nonlinear equations with an example.

Random fixed point theorems under weak topology features and application to random integral equations with lack of compactness

We present several random fixed point theorems for random operators with deterministic or stochastic domains. The main assumptions of our results are formulated in terms of the weak topology and an axiomatic definition of the measure of weak noncompactness. The results herein extend in a broad sense some new and classical results in the literature. As an application, we discuss the solvability of a random Hammerstein integral equation with lack of compactness.

Spectral properties for generalized weakly S-demicompact operators

In this paper, we introduce the concept of generalized weakly S-demicompact operators with respect to a weakly closed linear operator S. We study the general setting of Fredholm theory. We give some perturbation results on the behaviour of relative essential spectra of the sum of two bounded linear operators by means of the relative essential spectra of each one. A characterization of generalized weakly S-demicompact operators by means of measures of weak noncompactness is given. Moreover, we impose some sufficient conditions on the inputs of a closable block operator matrix to ensure the generalized weak S-demicompactness of its closure.

Fixed point theorems in WC-Banach algebras and their applications to infinite systems of integral equations

The paper is devoted to prove a few fixed point theorems for operators acting in WC-Banach algebras and satisfying some conditions expressed in terms of a generalized Lipschitz continuity and measures of weak noncompactness. Moreover, the assumptions imposed on the mentioned operators are formulated with help of weak topology and weak sequential continuity. Our fixed point results will be illustrated by proving the existence of solutions of an infinite system of nonlinear integral equations.

Measure of Weak Noncompactness and Fixed Point Theorems in Banach Algebras with Applications

In this paper, we prove some fixed point theorems for the nonlinear operator A · B + C in Banach algebra. Our fixed point results are obtained under a weak topology and measure of weak noncompactness; and we give an example of the application of our results to a nonlinear integral equation in Banach algebra.

A QUANTITATIVE EXTENSION OF SZLENK’S THEOREM

We show that for a bounded subset $A$ of the $L_{1}(\unicode[STIX]{x1D707})$ space with finite measure $\unicode[STIX]{x1D707}$, the measure of weak noncompactness of $A$ based on the convex separation of sequences coincides with the measure of deviation from the Banach–Saks property expressed by the arithmetic separation of sequences. A similar result holds for a related quantity with the alternating signs Banach–Saks property. The results provide a geometric and quantitative extension of Szlenk’s theorem saying that every weakly convergent sequence in the Lebesgue space $L_{1}$ has a subsequence whose arithmetic means are norm convergent.

Hybrid Fixed-Set Results for Multivalued Mappings in Banach Algebras under a Weak Topology Setting

In this paper, using the technique of measure of weak noncompactness and by removing the convexity hypothesis, we prove some fixed set results for the sum and the product of three multivalued mappings AB + C, acting on Banach algebras satisfying a certain sequential condition in the weak topology setting. In addition, by using a new definition of the multivalued mapping , we get new fixed set theorems for the mappings of the form under some suitable conditions on the operators A, B, and C in Banach algebras. These hybrid theorems improve some recently obtained results by Ben Amar et al. We also apply these results to the theory of self-similarity.

Implicit coupled Hilfer\u2013Hadamard fractional differential systems under weak topologies

In this article, we present some existence of weak solutions for a coupled system of implicit fractional differential equations of Hilfer–Hadamard type. Our approach is based on Mönch’s fixed point theorem associated with the technique of measure of weak noncompactness.

Existence of Weak Solutions for Fractional Integrodifferential Equations with Multipoint Boundary Conditions

By combining the techniques of fractional calculus with measure of weak noncompactness and fixed point theorem, we establish the existence of weak solutions of multipoint boundary value problem for fractional integrodifferential equations.

Existence and quantum calculus of weak solutions for a class of two-dimensional Schr\xf6dinger equations in mathbb{C}_{+}

The aim of this paper is to investigate the existence of weak solutions for a two-dimensional Schrödinger equation with a singular potential in mathbb{C}_{+}. Under appropriate assumptions on the nonlinearity, we introduce a new type of quantum calculus via the Morse theory and variational methods. By applying Schrödinger type inequalities and the well-known Banach fixed point theorem in conjunction with the technique of measures of weak noncompactness, the new and more accurate estimations for boundary behaviors of them are also deduced.

Coupled Pettis-Hadamard Fractional Differential Systems with Retarded and Advanced Arguments

In this study, we present some results concerning the existence of weak solutions for some coupled systems of Hadamard fractional differential equations involving the both retarded and advanced arguments. Our results are obtained by using fixed point theory and the technique of measure of weak noncompactness.

Measures of weak noncompactness and fixed point theory in Banach algebras satisfying condition (<i>P</i>)

Measures of weak noncompactness and fixed point theory in Banach algebras satisfying condition (<i>P</i>)

Weak Solutions for Partial Random Hadamard Fractional Integral Equations with Multiple Delays

We present some results concerning the existence of weak solutions for some functional integral equations of Hadamard fractional order with random effects and multiple delays by applying Mönch’s and Engl’s fixed point theorems associated with the technique of measure of weak noncompactness.

Measures of weak noncompactness, nonlinear leray-schauder alternatives in banach algebras satisfying condition (p) and an application

In this paper, we establish some new nonlinear Leray-Schauder alternatives for the sum and the product of weakly sequentially continuous operators in Banach algebras satisfying certain sequential condition (P). The main condition in our results is formulated in terms of axiomatic measures of weak noncompactness. As an application, our results are used to prove the existence of solutions for a nonlinear integral equation.

On the Existence of Weak Solutions of Nonlinear Integral Equations in Banach Spaces

In this paper, we use the techniques of measure of weak noncompactness and Henstock–Kurzweil–Pettis integrals to discuss the existence theorem of weak solutions for a class of the nonlinear integral equations and obtain a new result, which improves and extends some relevant results for differential and integral equations in Banach spaces.

On an integral equation under Henstock–Kurzweil–Pettis integrability

In this paper, we investigate the set of solutions for nonlinear Volterra type integral equations in Banach spaces in the weak sense and under Henstock–Kurzweil–Pettis integrability. Moreover, a fixed point result is presented for weakly sequentially continuous mappings defined on the function space C(K, X), where K is compact Hausdorff and X is a Banach space. The main condition is expressed in terms of axiomatic measure of weak noncompactness.