$\mathscr{I}_\lambda$-statistical limit points and $\mathscr{I}_\lambda$-statistical cluster points
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Abstract
In this paper we have extended the notion of $\lambda$-statistical limit points of real sequences to $\mathscr{I}_\lambda$-statistical limit points and studied some basic properties of the set of all $\mathscr{I}_\lambda$-statistical limit points and $\mathscr{I}_\lambda$-statistical cluster points of real sequences including their interrelationship. Then we have established $\mathscr{I}_\lambda$-statistical analogue of the monotone sequence theorem. Also introducing additive property of $\mathscr{I}_\lambda$-density zero sets we have established its relationship with $\mathscr{I}_\lambda$-statistical convergence.
Keywords:
$\mathscr{I}_\lambda$ -statistical convergence, $\mathscr{I}_\lambda$ -statistical limit point, $\mathscr{I}_\lambda$-statistical cluster point, $\mathscr{I}_\lambda $-density, $\mathscr{I}_\lambda$ -statistical boundednessMathematics Subject Classification:
Mathematics- Pages: 331-337
- Date Published: 01-01-2021
- Vol. 9 No. 01 (2021): Malaya Journal of Matematik (MJM)
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