Some Paranormed Double Difference Sequence Spaces for Orlicz Functions and Bounded-Regular Matrices

Abstract

The aim of this paper is to introduce some new double difference sequence spaces with the help of the Musielak-Orlicz functionℱ=(Fjk)and four-dimensional bounded-regular (shortly,RH-regular) matricesA=(anmjk). We also make an effort to study some topological properties and inclusion relations between these double difference sequence spaces.

Some Generalized Difference Sequence Spaces Defined by a Sequence of Moduli inn-Normed Spaces

“…Taking V = = 1, we get the spaces ∞ (Δ), (Δ), and 0 (Δ) introduced and studied by Kızmaz [8]. For more details about difference sequence spaces, see [15][16][17][18][19].…”

Some classes of ideal convergent sequences and generalized difference matrix operator

“…For some recent work related to Orlicz sequence spaces, we refer to Alotaibi et al [1], Mohiuddine et al [18,19], Savaş [23] and references therein.…”

Some New Lacunary Strong Convergent Vector-Valued Sequence Spaces

“…Over the years and under different names, statistical convergence has been discussed in the theory of Fourier analysis, ergodic theory, and number theory. Later on, it was further investigated from the sequence space point of view and linked with summability theory by Fridy [18], Connor [19],Šalát [20], Mursaleen and Edely [21], Isk [22], Mohiuddine and Alghamdi [23], Hazarika et al [24], Kolk [25], Maddox [26], Alotaibi and Mursaleen [27], Mohiuddine et al [28], Mohiuddine and Aiyub [29], and many others. In recent years, generalizations of statistical convergence have appeared in the study of strong integral summability and the structure of ideals of bounded continuous functions on locally compact spaces.…”