Measures of noncompactness
Application of measures of noncompactness to the infinite system of second order differential equations in \(\ell {p}\) spaces
... of noncompactness endow helpful information, which is extensively used in the theory of integral and integro-differential ...well-known measures of noncompactness are the Kuratowski measure (α), the ...
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On local attractivity of nonlinear functional integral equations via measures of noncompactness
... via measures of noncompactness by many researchers (see, for instance, Banas and Goebel [3], Banas and Rzepka [4], Dhage [8, 9], Dhage and Ntouyas [13] and the references ...of measures of ...
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Construction of measures of noncompactness of \(\mathit{DC}^{n}[J,E]\) and \(C^{n} {0}[J,E]\) with application to the solvability of nth order integro differential equations in Banach spaces
... hand, measures of noncompactness are very useful tools in functional anal- ysis, for instance in metric fixed point theory and in the theory of operator equations in Banach ...
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An application of measures of noncompactness in the investigation of boundedness of solutions of second order neutral difference equations
... of measures of noncompactness can be found in the book of Akhmerov et ...defined measures of noncompactness as presented in paper [] by Banaś and ...2 Measures of noncompactness ...
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Measures of noncompactness in spaces of regulated functions with application to semilinear measure driven equations
... In this paper, the issue on abstract semilinear measure driven equations in Banach spaces with nonlocal conditions has been addressed for the first time, which can model a large class of hybrid systems with Zeno behavior. ...
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Convex Solutions of a Nonlinear Integral Equation of Urysohn Type
... of noncompactness are frequently used in nonlinear analysis, in branches such as the theory of differential and integral equations, the operator theory, or the approximation ...of noncompactness see, ...of ...
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Generalization of Darbo's fixed point theorem and application
... the measures of noncompactness in the form of axiomatic ways in ...the measures of noncompactness solves the above problems to a great extent ...the measures of noncompactness, ...
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Measure of noncompactness and application to stochastic differential equations
... It has been found over the years that the fixed point theory is a powerful tool for the resolu- tion of nonlinear problems (differential equations, integro-differential equations, . . .). The roots of this theory go back to ...
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Fixed point theorems and the Krein-S̆mulian property in locally convex spaces
... The aim of this paper is to establish some new fixed point theorems for the superposition operators in locally convex spaces which satisfy the Krein-˘Smulian property. We employ a family of measures of ...
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Existence of mild solutions for Sobolev-type Hilfer fractional evolution equations with boundary conditions
... On the other hand, a Sobolev-type equation appears in a variety of physical problems such as flow of fluid through fissured rocks, thermodynamics, propagation of long waves of small amplitude and so on [37–39]. The ...
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Hausdorff measure of noncompactness in some sequence spaces of a triple band matrix
... In this paper, we establish some identities or estimates for the operator norms and the Hausdorff measures of noncompactness of certain matrix operators on the spaces c0 B, ∞ B and by usi[r] ...
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Positive solutions of fractional integral equations by the technique of measure of noncompactness
... In the present study, we work on the problem of the existence of positive solutions of fractional integral equations by means of measures of noncompactness in association with Darbo’s fixed point theorem. To ...
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On abstract fractional integro-differential equations via measure of noncompactness
... decades, measures of non- compactness became inevitable procedure in nonlinear ...of measures of noncompactness, the two ones: the Kura- towski measure of noncompactness and the Hausdorff ...
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Stability for Functional Differential Equations with Delay in Banach Spaces
... Remark 1. It is clear that we can assume about the function G other types of continuity and other conditions on measures of noncompactness. When we investigate the existence of solutions of (1) with ...
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Compact matrix operators on a new sequence space related to \(\ell {p}\) spaces
... Proof The proof is elementary and left to the reader. Remark . The characterizations of matrix classes considered in this paper can easily be obtained as in Corollaries . and . of []. Thus, we shall omit these ...
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Leray-Schauder-type fixed point theorems in Banach algebras and application to quadratic integral equations
... The aim of this paper is to establish new fixed point theorems in Banach algebras relative to the weak topology under Leray-Schauder-type boundary conditions. Then, we replace the weak continuity of the involved operators ...
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A study of nonlocal problems of impulsive integrodifferential equations with measure of noncompactness
... Byszewski and Lakshmikantham [] showed the existence and uniqueness of mild solu- tions and classical solutions when f and g in (.) satisfy Lipschitz type conditions. Ntouyas and Tsamotas [, ] studied the case of ...
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\(F(\psi,\varphi)\) Contraction in terms of measure of noncompactness with application for nonlinear integral equations
... In this paper, some new generalization of Darbo’s fixed point theorem is proved by using a F( ψ , ϕ )-contraction in terms of a measure of noncompactness. Our result extends to obtaining a common fixed point for a ...
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A unified approach to nonlocal impulsive differential equations with the measure of noncompactness
... This paper is concerned with the existence of mild solutions to impulsive differential equations with nonlocal conditions. We firstly establish a property of the measure of noncompactness in the space of piecewise ...
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ON THE VOLTERRA-STIELTJES INTEGRAL EQUATION AND AXIOMATIC MEASURES OF WEAK NONCOMPACTNESS
... In last years the study of the integral equations of Volterra-Stieltjes type in a Banach space has been developed extensively. However almost all of the work was done using the strong topology (see [3]-[9]), while the ...
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