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Browsing by Author "Patterson, R.F."

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    Article
    An Orlicz Extension of Some New Sequence Spaces
    (EUT Edizioni Universita di Trieste, 2005) Savaş, E.; Patterson, R.F.
    The aim of this note is to introduce and study a new concept of lacunary σ-convergence with respect to an Orlicz function and examine some properties of the resulting sequence spaces. © 2005 EUT Edizioni Universita di Trieste.
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    Article
    Σ-Asymptotically Lacunary Statistical Equivalent Sequences
    (2006) Savaş, E.; Patterson, R.F.
    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 [χ] and [y] are Sσ,θ-asymptotically equivalent of multiple L provided that for every ε > 0 limr 1/hr {k ε Ir: xσκ(m)/yσk(m) - L ≥ ε} = 0 uniformly in m = 1, 2, 3,..., (denoted by x ∼ Sσ,θy) simply Sσ,θ -asymptotically equivalent, if L = 1. Using this definition we shall prove Sσ,θ-asymptotically equivalent analogues of Fridy and Orhan's theorems in [5] and analogues results of Das and Patel in [1] shall also be presented. © Versita Warsaw and Springer-Verlag Berlin Heidelberg 2006.