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On lacunary generalized difference sequence spaces defined by Orlicz functions in a seminormed space and delta m/q-lacunary statistical convergence

100%

Bhardwaj V. , Bala I.

tom Vol. 41, nr 2

415-424

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].

On Lacunary strong σ-convergence with respect to a sequence of φ-fuctions

100%

Başarir M.

2010

tom Nr 43

19-32

In this paper, we introduce some new sequence spaces combining with lacunary sequence, σ-convergence, a sequence of φ-functions and a sequence of modulus functions. We establish some inclusion relations between these spaces under some conditions. Also we studied connections between lacunary (A, φk, σ )-statistically convergence with these spaces.

Multiplier sequence spaces of fuzzy numbers defined by a Musielak-Orlicz function

84%

Raj K. , Gupta A.

2012

tom Vol. 35

69--81

In this paper we introduce some multiplier sequence spaces of fuzzy number by using a Musielak-Orlicz function ℳ = (Mk) and multiplier function u = (uk) and prove some inclusion relations between the resulting sequences spaces.

Asymptotically lacunary statistical equivalence of double sequences of sets

84%

Nuray F. , Patterson R. F. , Dündar E.

2016

tom Vol. 49, nr 2

183--196

The concepts of Wijsman asymptotically equivalence, Wijsman asymptotically statistically equivalence, Wijsman asymptotically lacunary equivalence and Wijsman asymptotically lacunary statistical equivalence for sequences of sets were studied by Ulusu and Nuray [24]. In this paper, we get analogous results for double sequences of sets.