In the present paper, we introduce the sequence space λ p of non-absolute type and prove that the spaces λ p and p are linearly isomorphic for 0 < p ≤ ∞. Further, we show that λ p is a p-normed space and a BK-space in the cases of 0 < p < 1 and 1 ≤ p ≤ ∞, respectively. Furthermore, we derive some inclusion relations concerning the space λ p. Finally, we construct the basis for the space λ p , where 1 ≤ p < ∞.

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a b s t r a c tThe concept of λ-statistical convergence was introduced in [M. Mursaleen, λ-statistical convergence, Math Slovaca, 50 (2000) 111-115] by using the generalized de la Vallée Poussin mean. In this work we apply this method to prove some Korovkin type approximation theorems.

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