GENERALIZED DIFFERENCE SEQUENCE SPACE DEFINED BY |(N)over-bar, pk| SUMMABILITY AND AN ORLICZ FUNCTION IN SEMINORMED SPACE

The object of this paper is to introduce a new difference sequence space which arise from the notions of |(N) over bar, p(k)| summability and an Orlicz function in seminormed complex linear space. Various algebraic and topological properties and certain inclusion relations involving this space have been discussed. This study generalizes results: [ALTIN, Y.- ET, M.-TRIPATHY, B. C.: The sequence space |(N) over barp| (M,r,q,s) on seminormed spaces, Appl. Math. Comput. 154 (2004), 423-430], [BHARDWAJ, V. K.-SINGH, N.: Some sequence spaces defined by |(N) over bar, p(n)| summability, Demonstratio Math. 32 (1999), 539-546] and [BHARDWAJ, V. K.-SINGH, N.: Some sequence spaces defined by |(N) over bar, pn| summability and an Orlicz function, Indian J. Pure Appl. Math. 31 (2000), 319-325]. (C) 2010 Mathematical Institute Slovak Academy of Sciences