Strongly almost convergent generalized difference sequences associated with multiplier sequences

“…The concept of statistical convergence was introduced by Fast [1] and Schoenberg [2] independently. Many authors studied the concept of statistical convergence from the past few years we may refer to ( [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]) and references therein.…”

Section: Introductionmentioning

confidence: 99%

A Note on Lacunary Sequence Spaces of Fractional Difference Operator of Order $(α, β)$

Cai

Sharma

Mursaleen

2022

Journal of Function Spaces

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In the present paper, we defined lacunary sequence spaces of fractional difference operator of order α , β over n -normed spaces via Musielak-Orlicz function M = I k . Our aim in this paper is to study some topological properties and inclusion relation between the spaces I − N α β A , M , u , θ , Δ γ , · , ⋯ , · 0 , I − N α β A , M , u , θ , Δ γ , · , ⋯ , · , and I − N α β A , M , u , θ , Δ γ , · , ⋯ , · ∞ .

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“…Furthermore, Karakus and Basar introduced the multiplier spaces S (T), S w (T) and studied some new multiplier spaces by using generalization of almost summability in [18,19]. To know more about multiplier spaces, one may refer to [13,14,16,29]. Lorentz proved that a sequence z = (z k ) ∈ ∞ is said to be almost convergent to L ∈ C and is denoted by…”

Section: Introductionmentioning

confidence: 99%

Applications of Orlicz–Pettis theorem in vector valued multiplier spaces of generalized weighted mean fractional difference operators

2021

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In this study, we deal with some new vector valued multiplier spaces $S_{G_{h}}(\sum_{k}z_{k})$ S G h ( ∑ k z k ) and $S_{wG_{h}}(\sum_{k}z_{k})$ S w G h ( ∑ k z k ) related with $\sum_{k}z_{k}$ ∑ k z k in a normed space Y. Further, we obtain the completeness of these spaces via weakly unconditionally Cauchy series in Y and $Y^{*}$ Y ∗ . Moreover, we show that if $\sum_{k}z_{k}$ ∑ k z k is unconditionally Cauchy in Y, then the multiplier spaces of $G_{h}$ G h -almost convergence and weakly $G_{h}-$ G h − almost convergence are identical. Finally, some applications of the Orlicz–Pettis theorem with the newly formed sequence spaces and unconditionally Cauchy series $\sum_{k}z_{k}$ ∑ k z k in Y are given.

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Strongly almost convergent generalized difference sequences associated with multiplier sequences

Abstract: ABSTRACT. Let Λ = (λ k ) be a sequence of non-zero complex numbers. In this paper we introduce the strongly almost convergent generalized difference sequence spaces associated with multiplier sequences i.e.

Cited by 8 publications

References 15 publications

On lacunary Δ^m-statistical convergence of triple sequence in intuitionisticfuzzy normed space

On lacunary Δ^m-statistical convergence of triple sequence in intuitionisticfuzzy normed space

A Note on Lacunary Sequence Spaces of Fractional Difference Operator of Order $(α, β)$

Applications of Orlicz–Pettis theorem in vector valued multiplier spaces of generalized weighted mean fractional difference operators

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Strongly almost convergent generalized difference sequences associated with multiplier sequences

Abstract: ABSTRACT. Let Λ = (λ k ) be a sequence of non-zero complex numbers. In this paper we introduce the strongly almost convergent generalized difference sequence spaces associated with multiplier sequences i.e.

Cited by 8 publications

References 15 publications

On lacunary Δ^m-statistical convergence of triple sequence in intuitionisticfuzzy normed space

On lacunary Δ^m-statistical convergence of triple sequence in intuitionisticfuzzy normed space

A Note on Lacunary Sequence Spaces of Fractional Difference Operator of Orderα,β

Applications of Orlicz–Pettis theorem in vector valued multiplier spaces of generalized weighted mean fractional difference operators

Contact Info

Product

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A Note on Lacunary Sequence Spaces of Fractional Difference Operator of Order $(α, β)$