On Generalized Orlicz Sequence Spaces Defined by Double Sequences

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Dec 2015Publisher:Walter de Gruyter GmbHJournal:Fasciculi Mathematici, volume 55, pages 65-80 (eissn: 0044-4413,

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Authors: Kolk, Enno;

doi: 10.1515/fascmath-2015-0015

On Generalized Orlicz Sequence Spaces Defined by Double Sequences

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Abstract

Abstract S.D. Parashar and B. Choudhary defined in 1994 certain paranorms for some Orlicz sequence spaces. Their ideas are applied later for topologization of various generalized Orlicz sequence spaces. The author determines in 2011 some alternative F-seminorms (which are also paranorms) for such spaces. In this paper these results are extended to generalized Orlicz sequence spaces defined via double sequences..

Keywords

double sequence, paranorm, Orlicz function, \(\varphi\)-function, modulus function, strong summability, Absolute and strong summability, matrix method, Matrix methods for summability, sequence space, SM method, Convergence and divergence of series and sequences, \(F\)-seminorm, Sequence spaces (including Köthe sequence spaces)

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