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1
Content available remote Remarks on submultiplicative functions
EN
The real functions satisfying the inequality Ф (uv) ≤ KФ (u) Ф (v) for some positive K which occur among others in [5], [3], [4], and referred there as submultiplicative, are discussed. A simplifying remark that Ф satisfies this inequality iff KФ is submultiplicative in the standard sense, is done. It is shown that, under general conditions, the standard submultiplicativity of Ф and the inequality Ф (u) Ф (1/u) ≤ 1 imply that Ф must be multi-plicative. Applying a result of Bhatt [1], we observe that if p is a nontrivial seminorm on a Banach algebra X such that the set { [formula] .. : ∈ G X, p (x) ≠ 0} is a singleton {λ}, then s = λp is a submultiplicative seminorm on X.
EN
In this paper we define (...), the sequence spaces on a seminormed complex linear space, using an Orlicz function. We give various properties and some inclusion relations on this space.
3
Content available remote The semi normed space defined by a double gai sequence of modulus function
EN
In this paper we introduce the sequence spaces x2m(p, q, u), using an modulus function M and defined over a semi normed space (X, q); semi normed by q. We study some properties of these sequence spaces and obtain some inclusion relations.
4
Content available remote Some paranormed difference double sequence spaces defined by Orlicz function
EN
In this article we introduce some vector valued difference paranormed double sequence spaces defined by Orlicz function. We study some of their properties like solidness, symmetric-ity, completeness etc. and prove some inclusion results.
5
Content available remote Strongly (Vσ,θ, q] - summable sequences defined by Orlicz functions
EN
The purpose of this paper is to introduce the space of sequences those are strongly -summable with respect to an Orlicz function. We give some relations related to these sequence spaces. We also show that the spaces may be represented as a space.
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