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σ-asymptotically lacunary statistical equivalent sequences

Ekrem SavaşRichard Patterson — 2006

Open Mathematics

This paper presents the following definitions which is a natural combination of the definition for asymptotically equivalent, statistically limit, lacunary sequences, and σ-convergence. Let ϑ be a lacunary sequence; Two nonnegative sequences [x] and [y] are S σ,8-asymptotically equivalent of multiple L provided that for every ε > 0 lim r 1 h r k I r : x σ k ( m ) y σ k ( m ) - L = 0 uniformly in m = 1, 2, 3, ..., (denoted by x S σ , θ y) simply S σ,8-asymptotically equivalent, if L = 1. Using this definition we shall prove S σ,8-asymptotically equivalent...

On some consequences of a generalized continuity

Pratulananda DasEkrem Savaş — 2014

Archivum Mathematicum

In normed linear space settings, modifying the sequential definition of continuity of an operator by replacing the usual limit " lim " with arbitrary linear regular summability methods 𝐆 we consider the notion of a generalized continuity ( ( 𝐆 1 , 𝐆 2 ) -continuity) and examine some of its consequences in respect of usual continuity and linearity of the operators between two normed linear spaces.

Some sequence spaces defined by Orlicz functions

Ekrem SavaşRahmet Savaş — 2004

Archivum Mathematicum

In this paper we introduce a new concept of λ -strong convergence with respect to an Orlicz function and examine some properties of the resulting sequence spaces. It is also shown that if a sequence is λ -strongly convergent with respect to an Orlicz function then it is λ -statistically convergent.

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