Generalized difference sequence space defined by |$$ \bar N $$, p k| summability and an Orlicz function in seminormed space

Abstract

Abstract The object of this paper is to introduce a new difference sequence space which arise from the notions of |$$ \bar N $$, 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 |$$ \bar N_p $$|(M, r, q, s) on seminormed spaces, Appl. Math. Comput. 154 (2004), 423–430], [BHARDWAJ, V. K.—SINGH, N.: Some sequence spaces defined by |$$ \bar N $$, p n| summability, Demonstratio Math. 32 (1999), 539–546] and [BHARDWAJ, V. K.—SINGH, N.: Some sequence spaces defined by |$$ \bar N $$, p n| summability and an Orlicz function, Indian J. Pure Appl. Math. 31 (2000), 319–325].