The definition of lacunary strong convergence is extended to a definition of lacunary strong convergence with respect to a sequence of modulus functions in a Banach space. We study some connections between lacunary statistical convergence and lacunary strong convergence with respect to a sequence of modulus functions in a Banach space.
In this paper we study the set of statistical cluster points of sequences in -dimensional spaces. We show that some properties of the set of statistical cluster points of the real number sequences remain in force for the sequences in -dimensional spaces too. We also define a notion of -statistical convergence. A sequence is -statistically convergent to a set if is a minimal closed set such that for every the set has density zero. It is shown that every statistically bounded sequence...
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