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a b s t r a c tIn this paper we make a new approach to the notions of [V , λ]-summability and λ-statistical convergence by using ideals and introduce new notions, namely, I − [V , λ]-summability and I − λ-statistical convergence. We mainly examine the relation between these two new methods as also the relation between I − λ-statistical convergence and I-statistical convergence introduced by the authors recently. We carry out the whole investigation in normed linear spaces.

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In this paper we introduce a new concept for almost lacunary strong P-convergent with respect to an Orlicz function and examine some properties of the resulting sequence space. We also introduce and study almost lacunary statistical convergence for double sequences and we shall also present some inclusion theorems.

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