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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.
2
Content available remote Non-square points of Orlicz-Lorentz function spaces
EN
In this paper, criteria for non-square points in Orlicz-Lorentz function spaces Λφ,ω endowed with the Luxemburg norm are given. The widest possible classes of convex Orlicz functions and weight functions are admitted. In consequence, criteria for non-square points in Orlicz spaces Lφ, which generalize the already known results, are presented.
3
Content available Some strongly almost summable sequence spaces
EN
In the present paper we introduce some strongly almost summable sequence spaces using ideal convergence and Musielak-Orlicz function M = (Mk) in n-normed spaces. We examine some topological properties of the resulting sequence spaces.
4
Content available remote Some generalized double lacunary Zweier convergent sequence spaces
EN
We introduce generalized double lacunary Zweier convergent sequence spaces over n-normed spaces via a sequence of Orlicz functions. We alsomake an e×ort to study some topological properties and inclusion relations between these spaces. Furthermore, we study the concept of double lacunary statistical Zweier convergence over n-normed spaces.
EN
In the present paper we introduced some seminormed difference sequence spaces combining lacunary sequences and Musielak-Orlicz function M = (Mk) over n-normed spaces and examine some topological properties and inclusion relations between resulting sequence spaces.
6
Content available remote On generalized Orlicz sequence spaces defined by double sequences
EN
S.D. Parashar and B. Choudhary defined in 1994 certain paranorms for some Orlicz sequence spaces. Their ideas are applied later for topologization of various generalized Orlicz sequence spaces. The author determines in 2011 some alternative F-seminorms (which are also paranorms) for such spaces. In this paper these results are extended to generalized Orlicz sequence spaces defined via double sequences.
7
EN
In this paper, we introduce some new double sequence spaces with respect to an Orlicz function and define two new convergence methods related to the concepts of statistical convergence and lacunary statistical convergence for double sequences. We also present some inclusion theorems for our newly defined sequence spaces and statistical convergence methods.
EN
In the present paper we introduce some new generalized classes of difference sequence spaces of fuzzy numbers defined by a sequence of Orlicz functions. We also make an effort to study some topological properties and prove some inclusion relations between these spaces.
9
Content available remote K-extreme point of generalized Orlicz sequence spaces with Luxemburg norm
EN
In this paper,we give necessary and sufficient conditions in order that a point u∈S(l(Φ)) is a k-extreme point in generalized Orlicz sequence spaces equipped with the Luxemburg norm, combing the methods used in classical Orlicz spaces and new methods introduced especially for generalized ones. The results indicate the difference between the classical Orlicz spaces and generalized Orlicz spaces.
10
EN
In this article we introduce some statistically convergent difference double sequence spaces defined by Orlicz function. Completeness of the spaces will be proved. We study some of their other properties like solidness, symmetricity etc. and prove some inclusion results.
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.
EN
The idea of quasi almost P-convergent sequences defined as [...] was introduced by V.A.Khan and Q.M.D.Lohani [Mathematicki Vesnik, (60), 95-100 (2008)]. In this paper we introduce a new concept for quasi almost ∆m-lacunary strongly P-convergent double sequences defined by Orlicz function and give inclusion relations.
13
EN
In this paper, we define and examine some new difference sequence spaces combining with de la Vallee-Poussin mean and a sequence of Orlicz functions which completes the gap of the literature. We also introduce the concept of S -statistical convergent sequences and give some inclusion relations between these defined spaces with the space of -statistical convergent sequences.
14
Content available remote Some difference paranormed sequence spaces defined by Orlicz functions
EN
In this paper we introduce the difference paranormed sequence spaces ...[wzór] respectively. We study their different properties like completeness, solidity, monotonicity, symmetricity etc.We also obtain some relations between these spaces as well as prove some inclusion results.
15
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.
EN
The main purpose of this paper is to introduce a new concept of [...]-lacunary statistical convergence. It is shown that if a sequence is [...]-lacunary strongly summable with index p with respect to an Orlicz function M then it is A [...]-lacunary statistically convergent and that the concepts of [...]-lacunary strong summability with index p with respect to an Orlicz function M and [...]-lacunary statistical convergence are equivalent on [...]-bounded sequences. The composite space no [...] using composite Orlicz function Mv has also been introduced. It is also shown that if q is total, then every [...] method is consistent with the W[...] method. Our results generalize and unify the corresponding earlier results of Freedman et al. [5], Tripathy et al. [17, 18, 19] and, Bhardwaj and Singh [1].
17
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.
19
Content available remote Some sequence spaces defined by Orlicz functions
EN
The object of this paper is to introduce a new concept of lacunary strong convergence with respect to an Orlicz function and examine some properties of the resulting sequence spaces. We establish some elementary connections between lacunary strong convergence and lacunary strong convergence with respect to an Orlicz function which satisfies l2-condition. It is also shown that if a sequence is lacunary strongly convergent with respect to an Orlicz function then it is lacunary statistically convergent. In addition, lacunary strong convergence with respect to an Orlicz function is compared to other summability methods.
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