Abstract
The idea of difference sequence spaces was introduced by Kizmaz [14] and this concept was generalized by Et and Colak [6] . Recently the difference sequence spaces have been studied in (see, [3] , [7] , [17] , [18]). The purpose of this article is to introduce the sequence spaces using a modulus function f and more general C λ − method in viev of Armitage and Maddox [2]. Several properties of these spaces, and some inclusion relations have been examined.
Highlights
The notion of a modulus was introduced by Nakano [19]
Later on using a modulus different sequence spaces have been studied by Altın and Et [1], Et [5], Nuray and Savas [20], Tripathy and Chandra [26] and many others
The notion of difference sequence spaces was introduced by Kızmaz [14] and the notion was generalized by Et and Colak [6]
Summary
The notion of a modulus was introduced by Nakano [19]. We recall that a modulus f is a function from [0,∞) to [0,∞) such that i) f (x) = 0 if and only if x = 0, ii) f (x + y) ≤ f (x) + f (y) for x, y ≥ 0, iii) f is increasing, iv) f is continuous from the right at 0.It follows that f must be continuous everywhere on [0, ∞). Maddox [15] and Ruckle [22] used a modulus function to construct some sequence spaces. The notion of difference sequence spaces was introduced by Kızmaz [14] and the notion was generalized by Et and Colak [6].
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