Generalized difference sequence spaces on seminormed space defined by Orlicz functions

Abstract

ABSTRACT. In this paper we define the sequence space M (∆ m , p, q, s) on a seminormed complex linear space by using an Orlicz function. We study its different algebraic and topological properties like solidness, symmetricity, monotonicity, convergence free etc. We prove some inclusion relations involving M (∆ m , p, q, s).

<b>Almost Statistical Convergence of Order alpha

“…The space M  with the norm Bhardwaj and Singh (2000), Mursaleen et al (2001), Savaş and Rhoades (2002), Çolak et al (2006), Et et al (2006), Güngör et al (2004), Tripathy et al (2008), Dutta and Başar (2011) and …”

On Zweier generalized difference ideal convergent sequences in a locally convex space defined by Musielak-Orlicz function

“…Subsequently Orlicz function was used to define sequence spaces by Parashar and Choudhary [31] and many others (see [9,26,28,38]). Remark 1.1.…”

On certain Euler difference sequence spaces of fractional order and related dual properties

“…In fact, this difference matrix includes several difference matrices introduced by Ahmad and Mursaleen [1], Malkowsky et al [18] and many others (see [5,10,14,15,16,17,19,20,23]). The well known Euler mean matrix E r = (e r nk ) of order r, (0 < r < 1) is defined by the matrix…”