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Invariant means and lacunary sequence spaces of order (α, β)

Demonstratio Mathematica
In this article, we use the notion of lacunary statistical convergence of order (α,β)\left(\alpha ,\beta ) to introduce new sequence spaces by lacunary sequence, invariant means defined by Musielak-Orlicz function ℳ=(ℵk){\mathcal{ {\mathcal M} }}=\left({\
Ayman-Mursaleen Mohammad, Nasiruzzaman Md., Sharma Sunil K., Cai Qing-Bo   +3 more
doaj   +3 more sources

On Lacunary $\mathcal{I}_2^{\ast }$-Convergence and Lacunary $\mathcal{I}_2^{\ast }$-Cauchy Sequence

Communications in Advanced Mathematical Sciences, 2023
In the study conducted here, we have given some new concepts in summability. In this sense, firstly, we have given the concept of lacunary $\mathcal{I}_2^{\ast}$-convergence and we have investigated the relations between lacunary $\mathcal{I}_2 ...
Nimet Pancaroğlu Akın, Erdinç Dündar
doaj   +2 more sources

Lacunary ℐ-Invariant Convergence of Sequence of Sets in Intuitionistic Fuzzy Metric Spaces

Journal of Mathematics, 2021
The concepts of invariant convergence, invariant statistical convergence, lacunary invariant convergence, and lacunary invariant statistical convergence for set sequences were introduced by Pancaroğlu and Nuray (2013).
Mualla Birgül Huban
doaj   +2 more sources

On Strongly Lacunary $\mathcal{I}_2^{\ast }$-Convergence and Strongly Lacunary $\mathcal{I}_2^{\ast }$-Cauchy Sequence

Universal Journal of Mathematics and Applications, 2023
In the study conducted here, we have given some new concepts in summability theory. In this sense, firstly, using the lacunary sequence we have given the concept of strongly $\mathcal{I}_{\theta_2}^{\ast}$-convergence and we have examined the relations ...
Esra Gülle, Nimet Pancaroğlu Akın, Erdinç Dündar   +2 more
doaj   +2 more sources

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

Journal of Function Spaces, 2022
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=Ik.
Qing-Bo Cai, Sunil K. Sharma, Mohammad Ayman Mursaleen   +2 more
doaj   +2 more sources

Centered Polygonal Lacunary Sequences [PDF]

Mathematics, 2019
Lacunary functions based on centered polygonal numbers have interesting features which are distinct from general lacunary functions. These features include rotational symmetry of the modulus of the functions and a notion of polished level sets.
Keith Sullivan, Drew Rutherford, Darin J. Ulness   +2 more
doaj   +2 more sources

Strongly Almost Lacunary -Convergent Sequences [PDF]

Abstract and Applied Analysis, 2013
We study some new strongly almost lacunary -convergent generalized difference sequence spaces defined by an Orlicz function. We give also some inclusion relations related to these sequence spaces.
Adem Kılıçman, Stuti Borgohain
doaj   +5 more sources

Some new lacunary statistical convergence with ideals [PDF]

Journal of Inequalities and Applications, 2017
In this paper, the idea of lacunary I λ $I_{\lambda}$ -statistical convergent sequence spaces is discussed which is defined by a Musielak-Orlicz function.
Adem Kilicman, Stuti Borgohain
doaj   +2 more sources

Rough I2 ${I}_{2}$-lacunary statistical convergence of double sequences [PDF]

Journal of Inequalities and Applications, 2018
In this paper, we introduce and study the notion of rough I2 $\mathcal {I}_{2}$-lacunary statistical convergence of double sequences in normed linear spaces.
Ömer Kişi, Erdinç Dündar
doaj   +2 more sources

On lacunary invariant sequence spaces defined by a sequence of modulus functions [PDF]

Applied Mathematics and Computation, 2004
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Vatan Karakaya
exaly   +6 more sources