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Generalized strongly \((V,\lambda)\)- summable sequences defined by Orlicz functions. (English) Zbl 1088.40002
In 1981 H. Kizmaz [Can. Math. Bull. 24, 169–176 (1981; Zbl 0454.46010)] introduced the notion of difference sequence spaces and this concept was generalized by M. Et and R. Çolak [Soochow J. Math. 21, 377–386 (1995; Zbl 0841.46006)] in 1995. In this paper the concepts of \(\kappa ^m\)-statistical convergence and strongly \((V,\kappa)(\Delta ^m)\)-summable sequence with respect to an Orlicz function are introduced. The paper consists of three sections. The first section is an introduction and gives the necessary definitions which are used in the latter two sections. The second section deals with \(\kappa ^m\)-statistical convergence where some inclusion relations are given. Some topological properties of three sequence spaces defined by using an Orlicz function \(M\) are introduced and examined in the third section. It is shown that if a sequence is strongly \((V,\kappa)(\Delta ^m)\)-summable with respect to an Orlicz function, then it is \(S_{\kappa ^m}\)-statistically convergent.

MSC:
40C05 Matrix methods for summability
46A45 Sequence spaces (including Köthe sequence spaces)
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