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On a new sequence space related to the Orlicz sequence space

Khan V. A.

Journal of Mathematics and Applications

2008

Vol. 30

61-69

The space m(Φ) was introduced by sargent[14]and further studied by Malkowsky and Mursaleen [8] and Mursaleen [9]. In this paper we extend this space to m(M, Φ, p) and study some of its properties, inclusions relations and its relation with the Orlicz sequence space l(sub M).

Diffrerence sequence spaces defined by Orlicz functions

Mursaleen, Khan A., Qamaruddin

Demonstratio Mathematica

1999

Vol. 32, nr 1

145-150

The idea of difference sequences was introduced by H. Kizmaz [1] . In this paper we define some difference sequence spaces by Orlicz Function and establish some inclusion relations.

Weak-sequential compactness on non-locally convex Orlicz spaces

Nowak M.

Bulletin of the Polish Academy of Sciences. Mathematics

1998

Vol. 46, no 3

225-231

Let [L^fi] be an Orlicz space defined by a finite valued Orlicz function [fi] (not necesarilly convex) over a [sigma]-finite atomless measure space. Let (L^fi[...] be the order continous dual of [L^fi]. It is proved that a subset Z of [L^fi] is conditionally sequentially sigma([L^fi],(L^fi])[...)-compact (i.e., every sequence in Z contains a sigma([L^[fi],(L^fi])[...])-Cauchy subsequence) if and only if Z is norm bounded in some Orlicz space [L^psi] where psi increases more rapidly than [...] (the convex minorant of fi).