Invariant and Lacunary Invariant Statistical Equivalence of Order β for Double Set Sequences

Abstract

In this study, as a new approach to the concept of asymptotical equivalence in the Wijsman sense for double set sequences, the new concepts which are called asymptotical invariant statistical equivalence of order β and asymptotical lacunary invariant statistical equivalence of order β (0<β≤1) in the Wijsman sense for double set sequences are introduced and explained with examples. In addition, the existence of some relations between these concepts and furthermore, the relationships between these concepts and previously studied asymptotical equivalence concepts in the Wijsman sense for double set sequences are investigated.

Keywords

• Asymptotical equivalence
• Convergence in the Wijsman sense
• Double lacunary sequence
• Invariant statistical convergence
• Order β
• Sequences of sets
• Sequences of sets

Çift Küme Dizileri için β ıncı Mertebeden İnvaryant ve Lacunary İnvaryant İstatistiksel Denklik

Abstract

Bu çalışmada, çift küme dizileri için Wijsman anlamında asimptotik denklik kavramına yeni bir yaklaşım olarak, çift küme dizileri için Wijsman anlamında β (0<β≤1) yıncı mertebeden asimptotik invaryant istatistiksel denklik ve asimptotik lacunary invaryant istatistiksel denklik olarak adlandırılan yeni kavramlar tanıtıldı ve örneklerle açıklandı. Ayrıca, bu kavramlar arasında bazı ilişkilerin varlığı ve dahası bu kavramlar ve daha önceden çift küme dizileri için Wijsman anlamında çalışılmış asimptotik denklik kavramları arasındaki ilişkiler incelendi.   

Keywords

• Asimptotik denklik; Wijsman anlamında yakınsaklık; Çift lacunary dizi; İnvaryant istatistiksel yakınsaklık; β ıncı mertebe; Küme dizisi.

References

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