On asymptotically generalized statistical equivalent sequences via ideals

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Published: Sep 30, 2012
DOI: https://doi.org/10.5556/j.tkjm.43.2012.919
Keywords:
Asymptotically equivalent sequences statistical convergence statistical convergence and ideal convergence

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Vijay Kumar Kaushik
Department ofMathematics, Haryana College of Technology andManagement, Kaithal-136027, Haryana, India.
Archana Sharma
Haryana College of Technology and Management, Kaithal, Haryana, India

Abstract

For an admissible ideal ${\mathcal I}\subseteq {\mathcal P}({\mathbb N})$ and a non-decreasing realsequence $\lambda =(\lambda_n)$ tending to $\infty$ with $\lambda_{n+1} \leq \lambda_n+1, \lambda_1 = 1$, the objective of this paper is to introduce the new notions ${\mathcal I}-$statistically equivalent, ${\mathcal I}-[V, \lambda]-$equivalent and ${\mathcal I}-\lambda -$statistically equivalent. which are natural combinations of the definitions for asymptotically equivalent, statistical limit, $\lambda-$statistical limit and ${\mathcal I}-$limit for number sequences. In addition, some relations among these new notions are also obtained.

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How to Cite
Kaushik, V. K., & Sharma, A. (2012). On asymptotically generalized statistical equivalent sequences via ideals. Tamkang Journal of Mathematics, 43(3), 469–478. https://doi.org/10.5556/j.tkjm.43.2012.919
Issue
Vol. 43 No. 3 (2012)
Section
Papers
Author Biography

Vijay Kumar Kaushik, Department ofMathematics, Haryana College of Technology andManagement, Kaithal-136027, Haryana, India.

Department ofMathematics, Haryana College of Technology andManagement, Kaithal-136027, Haryana, India.

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