The sequence space |Np|(M, r, q, s) on seminormed spaces

Abstract In this paper we define the space | N p |(M,r,q,s) on seminormed complex linear space by using an Orlicz function and we study various properties and obtain some inclusion relations involving this space. This study generalizes some results of Bhardwaj and Singh [Demonstratio Math. 32 (1999) 539; Indian J. Pure Appl. Math. 31 (2000) 319].

[1]  V. Bhardwaj,et al.  SOME SEQUENCE SPACES DEFINED BY \N,pn\ SUMMABILITY , 1999 .

[2]  I. J. Maddox.  Sequence spaces defined by a modulus , 1986, Mathematical Proceedings of the Cambridge Philosophical Society.

[3]  Manjul Gupta,et al.  Sequence spaces and series , 1981 .

[4]  Joram Lindenstrauss,et al.  On orlicz sequence spaces , 1971 .

[5]  L. A. Li︠u︡sternik,et al.  Elements of Functional Analysis , 1962 .

[6]  William H. Ruckle,et al.  FK Spaces in Which the Sequence of Coordinate Vectors is Bounded , 1973, Canadian Journal of Mathematics.

[7]  I. J. Maddox,et al.  Elements of functional analysis , 1971 .