On a New Sequence Space Defined by Orlicz Functions

Abstract

Abstract. The sequence space was introduced and studied by Mursaleen [9]. In this paper we extend to ( ) and study some properties and inclusion relations on this space.

On Certain Topological Structures of Summable Paranormed Sequence Space Defined in Two - Normed Space

“…Parasar and Choudhary (1994), Bhardwaj and Bala 2007), Khan (2008), Basariv and Altundag (2009), Tiwari and Srivastava (2010), Pahari ( , 2013Pahari ( , 2013Pahari ( , 2014Pahari ( & 2014 , and many others further studied various types of paranormed sequence spaces and function spaces.…”

On a New I-Convergent Double-Sequence Space

“…For the first time, Iconvergence was studied by Kostyrko et al [24]. Later on, it was studied byŠalát et al [25,26], Tripathy and Hazarika [27], Ebadullah et al [18][19][20]28], and Vakeel et al [1,29].…”

On Certain Topological Structures of Product Normed Space Valued Paranormed Space of Summable Sequences

“…Any subspace of ω is then called a sequence space. The various types of vector valued sequence spaces has been significantly developed by several workers for instances, Köthe (1970), Maddox (1980), Kamthan and Gupta (1980), Ruckle (1981), Malkowski and Rakocevic (2004), Khan (2008), Kolk (2011), , 2012& 2013. The notion of paranormed space is closely related to linear metric space (Wilansky, 1978).…”

“…The studies of paranorm on sequence spaces were initiated by Maddox (1969). Various types of paranorms on the spaces of sequences and functions were further studied in the works of Parashar and Choudhary (1994), Bhardwaj and Bala (2007), Khan (2008), Srivastava (2008 &2010), Pahari (2011Pahari ( & 2013, , 2012& 2013. Let (A, || .…”