• Journal of applied mathematics & informatics
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• v.40 no.1_2
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• pp.327-339
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• 2022

In this paper, we introduce arithmetic ${\mathcal{I}}$-statistically convergent sequence space $A{\mathcal{I}}SC$, ${\mathcal{I}}$-lacunary arithmetic statistically convergent sequence space $A{\mathcal{I}}SC_{\theta}$, strongly ${\mathcal{I}}$-lacunary arithmetic convergent sequence space $AN_{\theta}[{\mathcal{I}}]$ and prove some inclusion relations between these spaces. Futhermore, we give ${\mathcal{I}}$-lacunary arithmetic statistical continuity. Finally, we define ${\mathcal{I}}$-Cesàro arithmetic summability, strongly ${\mathcal{I}}$-Cesàro arithmetic summability. Also, we investigate the relationship between the concepts of strongly ${\mathcal{I}}$-Cesàro arithmetic summability, strongly ${\mathcal{I}}$-lacunary arithmetic summability and arithmetic ${\mathcal{I}}$ -statistically convergence.

• Communications of the Korean Mathematical Society
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• v.24 no.2
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• pp.239-245
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• 2009

We estimate the positive real zeros of certain trinomial equations and then deduce zeros bounds of some lacunary polynomials.

• Journal of applied mathematics & informatics
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• v.40 no.3_4
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• pp.433-444
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• 2022

In the present paper, we introduce some new notions of Wijsman ${\mathcal{I}}$-statistical convergence with the use of Orlicz function, lacunary sequence and triple sequences of sets, and obtain some analogous results from the new definitions point of views.

• Kyungpook Mathematical Journal
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• v.52 no.4
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• pp.473-482
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• 2012

In this article we introduce the concepts of lacunary I-convergent sequences. We investigate its different properties like solid, symmetric, convergence free etc.

• Kyungpook Mathematical Journal
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• v.46 no.4
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• pp.591-595
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• 2006

In this paper, we define ${\Delta}^m$-Lacunary strongly convergent sequences defined by sequence of moduli and give various properties and inclusion relations on these sequence spaces.

• Journal of applied mathematics & informatics
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• v.40 no.1_2
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• pp.215-231
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• 2022

In this paper, for double set sequences, as a new approach to the notion of Wijsman asymptotical lacunary statistical equivalence of order 𝜂, we introduce new concepts which are called Wijsman asymptotical ${\mathcal{I}}_2$-lacunary statistical equivalence of order 𝜂 and Wijsman asymptotical strong ${\mathcal{I}}_2$-lacunary equivalence of order 𝜂 where 0 < 𝜂 ≤ 1. Also, some properties of these new concepts are investigated, and the existence of some relations between these and some previously studied asymptotical equivalence concepts for double set sequences is examined.

• Kyungpook Mathematical Journal
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• v.27 no.2
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• pp.173-179
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• 1987

In this article the absolute convergence of lacunary Fourier Coefficients Series is studied for Hilbert space valued functions. The considered functions arc assumed to be of either the modulus of continuity or the modulus of smoothness of order l which are considered only at a fixed point in [$-{\pi},{\pi}$]. On the other hand for values in weakly sequentially complete Banach space, the lacunary Fourier coefficients series is strongly unconditionally convergent. The results obtained here are a kind of a generalization of the results due to Kandil [4].

• Journal of applied mathematics & informatics
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• v.37 no.1_2
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• pp.37-52
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• 2019

In this paper we introduce a new concept for Riesz almost lacunary ${\chi}^3$ sequence spaces strong P - convergent to zero with respect to an Orlicz function and examine some properties of the resulting sequence spaces. We introduce and study statistical convergence of Riesz almost lacunary ${\chi}^3$ sequence spaces and some inclusion theorems are discussed.

• Honam Mathematical Journal
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• v.43 no.1
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• pp.100-114
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• 2021

In this study, we present some asymptotical invariant and asymptotical lacunary invariant equivalence types for double sequences via ideals using modulus functions and investigate relationships between them.

• Honam Mathematical Journal
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• v.43 no.2
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• pp.343-357
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• 2021

In the present paper, we introduce the concepts of $\mathcal{I}$-asymptotically statistical $\tilde{\phi}$-equivalence and $\mathcal{I}$-asymptotically lacunary statistical $\tilde{\phi}$-equivalence for triple sequences. Moreover, we give the relations between these new notions.