Generalized Vector Valued Sequence Spaces Defined by Orlicz Functions

10.6988/TOJIMS.201105.0137

Mahmut Işik

Orlicz function ； Seminorm ； Sequence spaces

Tamsui Oxford Journal of Information and Mathematical Sciences

27卷2期（2011 / 05 / 01）

137 - 148

英文

In this paper we introduce the vector valued sequence spaces w0 (M, θ, △(superscript m), Q, p, u), w1 (M, θ, △(superscript m), Q, p, u), w(subscript ∞) (M, θ, △(superscript m), and S(subscript θ)(△(superscript m subscript uq)) using an Orlicz function, the generalized difference operator △(superscript m) and the multiplier sequence u=(u(subscript k)) of non-zero complex numbers. We give some relations related to these sequence spaces. It is also shown that if a sequence is strongly lacunary △(superscript m subscript uq)-Cesaro summable with respect to the Orlicz function M then it is △(superscript m subscript uq)-statistically convergent.