On Asymptotically Ι -Lacunary statistical Equivalent Sequences of order α

Author: E. Savas

Abstract: This paper presents the following definition which is a natural combination of the definition for asymptotically equivalent of order $$α$$, where $$0 <α < 1, I-statistically$$ limit, and $$I-lacunary$$ statistical convergence. Let $$θ$$ be a lacunary sequence; the two nonnegative sequences $$x=(x_{k})$$ and $$y=(y_{k})$$ are said to be asymptotically $$I-lacunary$$ statistical equivalent of order $$α$$ to multiple $$L$$ provided that for every $$ε > 0$$, and $$δ > 0$$, $$\lbrace r\in \mathbb{N}: \frac{1}{h_r^a}|\lbrace k \in Ι_{r}:|\frac{x_{k}}{y_k} - L|≥ε \rbrace |≥δ \rbrace \inΙ $$, (denoted by $$ x \sim y $$ and simply asymptotically $$I-lacunary$$ statistical equivalent of order $$ α $$ if $$L=1$$ In addition, we shall also present some inclusion theorems.The study leaves some interesting open problems.

Pages: 38-41

DOI: 10.46300/9101.2022.16.7

International Journal of Mathematical Models and Methods in Applied Sciences, E-ISSN: 1998-0140, Volume 16, 2022, Art. #7