Abstract
In this paper we construct some difference new modular sequence spaces defined by a sequence of Orlicz functions over n-normed spaces. We also study several properties relevant to topological structures and interrelationship between these spaces.
Highlights
Al. [9] and Tripathy et al [30] have introduced a new type of generalized difference operators and unified those as follows
< ∞, for some ρ > 0 k=1 which is called as an Orlicz sequence space
The main purpose of this paper is to study some difference new modular sequence spaces defined by a sequence of Orlicz functions over n−normed spaces
Summary
Seema Jamwal and Kuldip Raj abstract: In this paper we construct some new difference modular sequence spaces defined by a sequence of Orlicz functions over n-normed spaces. The space lM is a Banach space with the norm It is shown in [15] that every Orlicz sequence space lM contains a subspace isomorphic to lp(p ≥ 1). In the later stage different Orlicz sequence spaces were introduced and studied by Parashar and Choudhary [25], Esi and Et [6], Tripathy and Mahanta [31], Mursaleen [21] and many others. For a given Musielak-Orlicz function M, the Musielak-Orlicz sequence space tM and its subspace hM are defined as follows; tM = x ∈ ω : IM(cx) < ∞ for some c > 0 , hM = x ∈ ω : IM(cx) < ∞ for all c > 0 , where IM is a convex modular defined by IM(x) = Mk(xk), x = (xk) ∈ tM
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