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Topologies in generalized Orlicz sequence spaces; Filomat
, 2011
"... In 1994 S.D. Parashar and B. Choudhary defined certain paranorms in some Orlicz sequence spaces of Maddox type. Their ideas are applied later by many authors for topologization of various generalized Orlicz sequence spaces. We determine alternative Fseminorms in such spaces by using the standard ar ..."
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In 1994 S.D. Parashar and B. Choudhary defined certain paranorms in some Orlicz sequence spaces of Maddox type. Their ideas are applied later by many authors for topologization of various generalized Orlicz sequence spaces. We determine alternative Fseminorms in such spaces by using the standard arguments of modular spaces theory and a result about the topologization of sequence spaces defined by modulus functions. 1 Notation and background Let N = {1, 2,...} and let K be the field of real numbers R or complex numbers C. We write limn, supn, infn and n instead of limn→∞, supn∈N, infn∈N and∑∞ n=1, respectively. By the symbol ι we denote the identity mapping ι(z) = z. The superposition of two mappings f and g is denoted by fg, i.e., (fg)(z) = f(g(z)). For two sequences x = (xk), y = (yk) we use the notation xy = (xkyk) provided that xkyk is determined for all k ∈ N. We also use the notation R+ = [0,∞) and ek = (eik)i∈N (k ∈ N), where eik = 1 if i = k and eik = 0 otherwise. In all definitions which contain infinite series we tacitly assume the convergence of these series. An Fspace is usually understood as a complete metrizable topological vector space over K. It is known that the topology of an Fspace E can be given by an Fnorm, i.e., by the functional g: E → R with the axioms (see [20], p. 13) (N1) g(0) = 0; (N2) g(x+ y) ≤ g(x) + g(y) (x, y ∈ E); (N3) α  ≤ 1 (α ∈ K), x ∈ E = ⇒ g(αx) ≤ g(x);
An Extension of Modular Sequence Spaces
"... The main aim of this paper is to present an extension of the modular sequence spaces by means of Cesàro mean of order one, to investigate several relevant algebraic and topological properties, and derive some other spaces in the sequel. ..."
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The main aim of this paper is to present an extension of the modular sequence spaces by means of Cesàro mean of order one, to investigate several relevant algebraic and topological properties, and derive some other spaces in the sequel.
Some New Sequence Spaces on Seminormed Spaces
, 2013
"... In this paper, we define the sequence spaces [V, λ,M, p, s]1 (φ, q), ..."
Acta Scientiarum
"... How to cite Complete issue More information about this article Journal's homepage in redalyc.org Scientific Information System ..."
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How to cite Complete issue More information about this article Journal's homepage in redalyc.org Scientific Information System