• 제목/요약/키워드: double lacunary sequence

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WIJSMAN LACUNARY IDEAL INVARIANT CONVERGENCE OF DOUBLE SEQUENCES OF SETS

  • Dundar, Erdinc;Akin, Nimet Pancaroglu
    • 호남수학학술지
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    • 제42권2호
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    • pp.345-358
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    • 2020
  • In this paper, we study the concepts of Wijsman lacunary invariant convergence, Wijsman lacunary invariant statistical convergence, Wijsman lacunary ${\mathcal{I}}_2$-invariant convergence (${\mathcal{I}}^{{\sigma}{\theta}}_{W_2}$), Wijsman lacunary ${\mathcal{I}}^*_2$-invariant convergence (${\mathcal{I}}^{\ast}^{{\sigma}{\theta}}_{W_2}$), Wijsman p-strongly lacunary invariant convergence ([W2Nσθ]p) of double sequence of sets and investigate the relationships among Wijsman lacunary invariant convergence, [W2Nσθ]p, ${\mathcal{I}}^{{\sigma}{\theta}}_{W_2}$ and ${\mathcal{I}}^{\ast}^{{\sigma}{\theta}}_{W_2}$. Also, we introduce the concepts of ${\mathcal{I}}^{{\sigma}{\theta}}_{W_2}$-Cauchy double sequence and ${\mathcal{I}}^{\ast}^{{\sigma}{\theta}}_{W_2}$-Cauchy double sequence of sets.

ON ALGEBRA OF LACUNARY STATISTICAL LIMIT OF DOUBLE SEQUENCES IN INTUITIONISTIC FUZZY NORMED SPACE

  • SHAILENDRA PANDIT;AYAZ AHMAD
    • Journal of applied mathematics & informatics
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    • 제41권3호
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    • pp.541-552
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    • 2023
  • In 2005, Patterson studied lacunary statistical convergence of double sequences of real numbers and, in 2009, Mursaleen introduced notion of lacunary statistical convergence of single sequences in intuitionistic fuzzy normed space. The current work intends to investigate the lacunary statistical convergence of double sequences and some significant conclusions on the algebra of the lacunary statistical limit of double sequences in intuitionistic fuzzy normed space. In addition, we have studied some examples to support the definitions.

ASYMPTOTICAL INVARIANT AND ASYMPTOTICAL LACUNARY INVARIANT EQUIVALENCE TYPES FOR DOUBLE SEQUENCES VIA IDEALS USING MODULUS FUNCTIONS

  • Dundar, Erdinc;Akin, Nimet Pancaroglu;Ulusu, Ugur
    • 호남수학학술지
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    • 제43권1호
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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.

RIESZ TRIPLE ALMOST LACUNARY χ3 SEQUENCE SPACES DEFINED BY A ORLICZ FUNCTION-I

  • SUBRAMANIAN, N.;Esi, Ayhan;AIYUB, M.
    • Journal of applied mathematics & informatics
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    • 제37권1_2호
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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.