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Some sequence spaces defined by a modulus

Serpil Pehlivan; Brian Fisher — 1995

Mathematica Slovaca

Lacunary strong convergence with respect to a sequence of modulus functions

Serpil Pehlivan; Brian Fisher — 1995

Commentationes Mathematicae Universitatis Carolinae

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.

Statistical cluster points of sequences in finite dimensional spaces

Serpil Pehlivan; A. Güncan; M. A. Mamedov — 2004

Czechoslovak Mathematical Journal

In this paper we study the set of statistical cluster points of sequences in $m$ -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 $m$ -dimensional spaces too. We also define a notion of $Γ$ -statistical convergence. A sequence $x$ is $Γ$ -statistically convergent to a set $C$ if $C$ is a minimal closed set such that for every $ϵ > 0$ the set ${k ρ (C, x_{k}) \geq ϵ}$ has density zero. It is shown that every statistically bounded sequence...

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Currently displaying 1 – 3 of 3

Some sequence spaces defined by a modulus

Lacunary strong convergence with respect to a sequence of modulus functions

Statistical cluster points of sequences in finite dimensional spaces