Strongly (Vλ,a,p) - Summable Sequence Spaces Defined by a Modulus

Abstract

We introduce the strongly (Vλ,A,p) ‐ summable sequences and give the relation between the spaces of strongly (Vλ,A,p) ‐ summable sequences and strongly (Vλ,A,p) ‐ summable sequences with respect to a modulus function when A = (α ik ) is an infinite matrix of complex numbers and ρ = (pi) is a sequence of positive real numbers. Also we give natural relationship between strongly (Vλ, A,p) ‐ convergence with respect to a modulus function and strongly Sλ (A) ‐ statistical convergence. Key words: De la Vallee‐Poussin mean, modulus function, statistical convergence.

On generalized sequence spaces defined by modulus functions

“…Corollary 3 permits to define, for example, an F-seminorm on the sequence [16], and an F-norm on the GS space c 0 [N θ , I, Φ, X] which is considered in [41] for a Banach space X. Corollary 3 also contains, as special cases, the results about the topologization of some sequence spaces of type c 0 [A, I, φ, p] from [10], [14], and [39].…”

“…Main theorems are applicable in the case if λ and Λ are strong summability domains of a non-negative matrix A = (a nk ). Some special cases of such spaces are considered, for example, in [1] - [4], [6] - [16], [19] - [25], [27], [28], [30], [31], [36], [38] - [41], [43], [45] and [48] - [51]). …”

Strongly(Vλ, A, Δn(vm),p, q)-summable sequence spaces defined by modulus function and statistical convergence

“…We write [2],Gunor et al [8], Savas [19] and others). The idea of modulus function was introduced by Nakano [15].…”

“…The Belgin [2], Kolack [10] Maddox [12,13],Öztürk and Bilgin [2], Ruckle [17] and others used a modulus function for defining some new sequence spaces.…”