Hausdorff measure of noncompactness of matrix mappings on Cesàro spaces

Applications of Hausdorff Measure of Noncompactness in the Spaces of Generalized Means

In this paper, we derive some identities for the Hausdorff measures of noncompactness of certain matrix operators on the sequence spaces X(r,s) of generalized means. Further, we apply the Hausdorff measure of noncompactness to obtain the necessary and sufficient conditions for such operators to be compact. Mathematics subject classification (2010): 46B15, 46B45, 46B50.

Connected Mappings of Hausdorff Spaces

Applications of Measure of Noncompactness in Matrix Operators on Some Sequence Spaces

and Applied Analysis 3 Lemma 1.4 see 2 . Let X ⊃ φ be a BK-space and Y any of the spaces c0, c, or ∞. If A ∈ X,Y , then ‖LA‖ ‖A‖ X, ∞ sup n ‖An‖X < ∞, 1.4 where ‖A‖ X, ∞ denotes the operator norm for the matrix A ∈ X, ∞ . Sargent 3 defined the following sequence spaces. Let C denote the space whose elements are finite sets of distinct positive integers. Given any element σ of C, we denote by c ...

Impulsive integrodifferential Equations and Measure of noncompactness

This paper is concerned with the existence of mild solutions for impulsive integro-differential equations with nonlocal conditions. We apply the technique measure of noncompactness in the space of piecewise continuous functions and by using Darbo-Sadovskii's fixed point theorem, we prove reasults about impulsive integro-differential equations for convex-power condensing operators.

Measure of noncompactness of operators and matrices on the spaces c and c0

whenever the series are convergent for all n≥ 1. For any given subsets X , Y of s, we will say that the operator represented by the infinite matrix A = (anm)n,m≥1 maps X into Y that is A∈ (X ,Y), if (i) the series defined by An(x)= ∑∞ m=1 anmxm are convergent for all n≥ 1 and for all x ∈ X ; (ii) Ax ∈ Y for all x ∈ X . If c ⊂ cA = {x : Ax ∈ c},A is conservative. Well-known necessary and suffici...