The first measure of noncompactness was defined by Kuratowski in 1930 and later the
Hausdorff measure of noncompactness was introduced in 1957 by Goldenštein et al. These …

In this paper we apply the technique of measures of noncompactness to the theory of infinite
system of differential equations in the Banach sequence spaces ℓp (1≤ p<∞). Our aim is to …

The main object of this paper is to introduce a new Banach space derived by using a matrix
operator which is comprised of Euler's totient function. Also, we determine α, β, γ-duals of …

In the present paper, we establish some identities or estimates for the operator norms and
the Hausdorff measures of noncompactness of certain operators given by infinite matrices …

We prove some general results for the determination of the β-duals of, and the
characterisations of matrix transformations on matrix domains of arbitrary triangles in FK …

‎ In the peresent paper‎,‎ by using generalized weighted mean and difference‎‎ matrix of order $
m, $ we introduce the sequence spaces $ X (u, v,\Delta^{(m)}) $‎,‎ where $ X $ is one of the …

Application of Measure of Noncompactness to Infinite Systems of Differential Equations Page
1 Canad. Math. Bull. Vol. 56 (2), 2013 pp. 388–394 http://dx.doi.org/10.4153/CMB-2011-170-7 …

For a sequence x=(xk), we denote the difference sequence by Δ x=(xk− xk− 1). Let u=(uk) k=
0∞ and v=(vk) k= 0∞ be the sequences of real numbers such that uk≠ 0, vk≠ 0 for all k∈ …

In this paper, we characterize the matrix classes (ℓ 1, ℓ p (F ˆ)) (ℓ_1,ℓ_p(F)) (1≤ p<∞
1≦p<∞), where ℓ p (F ˆ) ℓ_p(F) is some Fibonacci difference sequence spaces. We also …

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 …