Orlicz lacunary sequence spaces of 𝑙-fractional difference operators

Abstract

Recently, S. K. Mahato and P. D. Srivastava [A class of sequence spaces defined by 𝑙-fractional difference operator, preprint 2018, http://arxiv.org/abs/1806.10383] studied 𝑙-fractional difference sequence spaces. In this article, we intend to make a new approach to introduce and study some lambda 𝑙-fractional convergent, lambda 𝑙-fractional null and lambda 𝑙-fractional bounded sequences over 𝑛-normed spaces. Various algebraic and topological properties of these newly formed sequence spaces have been explored, and some inclusion relations concerning these spaces are also established. Finally, some characterizations of the newly formed sequence spaces are given.

Barrelled Weakly Köthe–Orlicz Summable Sequence Spaces

“…It is worth noting that several kinds of sequence spaces have already been investigated in the literature. Descriptions of some of them rely on infinite Köthe matrices (a i,j ) i,j∈N , some others rely on Cesàro operators, and others rely on different kinds of convergence or summability (see [1][2][3][4][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]).…”

“…Of course, Orlicz functions yield natural sequence spaces in the scalar-valued case. They are also used to construct vector-valued sequence spaces (see for example [11,17,19] and the references therein). The characterization of continuous dual or Köthe-Toeplitz dual are examples of the main issues authors are interested in (see, e.g., [21]).…”