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WIJSMAN LACUNARY IDEAL INVARIANT CONVERGENCE OF DOUBLE SEQUENCES OF SETS
( Erdinç Dündar ),( Nimet Pancaroğlu Akin ) 호남수학회 2020 호남수학학술지 Vol.42 No.2
In this paper, we study the concepts of Wijsman lacunary invariant convergence, Wijsman lacunary invariant statistical convergence, Wijsman lacunary I<sub>2</sub>-invariant convergence (I<sup>σθ</sup><sub>W2</sub>), Wijsman lacunary I<sub>2</sub>-invariant convergence (I<sup>σθ</sup><sub>W2</sub>), Wijsman p- strongly lacunary invariant convergence ([W<sub>2</sub>N<sub>σθ</sub>]<sub>p</sub>) of double sequence of sets and investigate the relationships among Wijsman lacunary invariant convergence, [W<sub>2</sub>N<sub>σθ</sub>]<sub>p</sub>, I<sup>σθ</sup><sub>W2</sub> and I<sup>σθ</sup><sub>W2</sub>. Also, we introduce the concepts of I<sup>σθ</sup><sub>W2</sub>-Cauchy double sequence and I<sup>σθ</sup><sub>W2</sub> - Cauchy double sequence of sets.
( Erdinç Dündar ),( Nimet Pancaroğlu Akin ),( Ugur Ulusu ) 호남수학회 2021 호남수학학술지 Vol.43 No.1
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.