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On some classes of sequences defined by sequences of Orlicz functions. (English) Zbl 1103.46003
Using a sequence of Orlicz functions, the authors introduce some new seminormed sequence spaces and obtain some inclusion relations involving these sequence spaces. They introduce $\triangle^m_{u_g}$-statistical convergence and give some inclusion relations between $\triangle^m_{u_g}$-statistically convergent sequences and $w_1(M, \triangle^m, u, g)$-summable sequences with respect to an Orlicz function. They also show that the space $S_{gu}(\triangle^m) \cap l_\infty (u_g, \triangle^m)$ may be represented as $w_1(M, \triangle^m , u, g) \cap l_\infty (u_g, \triangle^m)$ spaces.

46A45Sequence spaces
40A05Convergence and divergence of series and sequences
40C05Matrix methods in summability