Abstract
The aim of this paper is to introduce some generalized spaces of double sequences with the help of the Musielak-Orlicz function and four-dimensional bounded-regular (shortly, RH-regular) matrices over n-normed spaces. Some topological properties and inclusion relations between these spaces are investigated. MSC:40A05, 40D25.
Highlights
The aim of this paper is to introduce some generalized spaces of double sequences with the help of the Musielak-Orlicz function M = (Mjk) and four-dimensional bounded-regular matrices A = over n-normed spaces
Of the definitions of convergence commonly employed for double series, only that due to Pringsheim permits a series to converge conditionally
It is not surprising that many authors in dealing with the convergence of double sequences should have restricted themselves to the class of bounded sequences or, in dealing with the summability of double series, to the class of series for which the function whose limit is the sum of the series is a bounded function of i and j
Summary
Mohiuddine et al [ ] defined and studied some paranormed double difference sequence spaces for four-dimensional bounded-regular matrices and MusielakOrlicz functions. Let M = (Mjk) be a Musielak-Orlicz function, that is, M is a sequence of Orlicz functions and let A = (anmjk) be a nonnegative four-dimensional bounded-regular matrix. P-lim n,m nm anmjk Mjk ujk r s xjk ρ pjk j,k= ,
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