Applications of Hausdorff Measure of Noncompactness in the Spaces of Generalized Means
نویسندگان
چکیده
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.
منابع مشابه
Application of measures of noncompactness to infinite system of linear equations in sequence spaces
G. Darbo [Rend. Sem. Math. Univ. Padova, 24 (1955) 84--92] used the measure of noncompactness to investigate operators whose properties can be characterized as being intermediate between those of contraction and compact operators. In this paper, we apply the Darbo's fixed point theorem for solving infinite system of linear equations in some sequence spaces.
متن کاملSOME GEOMETRIC PROPERTIES OF DIFFERENCE SEQUENCE SPACES OF ORDER m DERIVED BY GENERALIZED MEANS AND COMPACT OPERATORS
We have introduced a new sequence space l(r,s,t, p;Δ(m) ) combining by using generalized means and difference operator of order m . Some topological properties as well as geometric properties namely Banach-Saks property of type p and uniform Opial property have been studied. Furthermore, the α -, β -, γ duals of this space are computed and also obtained necessary and sufficient conditions for s...
متن کاملSome B-difference Sequence Spaces Derived by Generalized Means and Compact Operators
Abstract. This paper presents new sequence spacesX(r, s, t, p;B) forX ∈ {l∞(p), c(p), c0(p), l(p)} defined by using generalized means and difference operator. It is shown that these spaces are complete paranormed spaces and the spaces X(r, s, t, p;B) for X ∈ {c(p), c0(p), l(p)} have Schauder basis. Furthermore, the α-, β-, γduals of these sequence spaces are computed and also obtained necessary...
متن کاملImpulsive 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.
متن کاملExistence of solutions of infinite systems of integral equations in the Frechet spaces
In this paper we apply the technique of measures of noncompactness to the theory of infinite system of integral equations in the Fr´echet spaces. Our aim is to provide a few generalization of Tychonoff fixed point theorem and prove the existence of solutions for infinite systems of nonlinear integral equations with help of the technique of measures of noncompactness and a generalization of Tych...
متن کامل