Some New Strongly Almost Summable Difference Sequence Spaces

Abstract

Sequences are indispensible to the pure and applied mathematicians, and thus, by extension, to all field of sciences. The idea o f difference sequence spaces was introduced in 1981, which has been generalized. The space of almost convergence sequences introduced in 1948 was generalized in 1978. Almost convergence difference sequence spaces have undergone series of gradual generalization. The purpose of this paper is to introduce the concept of m v  almost strongly summable difference sequence spaces with respect to a sequence of moduli on a seminorm q and to examine some properties of the three introduced sequence spaces which generalize many existing results, Various topological properties of these spaces with some of their inclusion relations, were studied including their solidity, symmetricity, sequence algebra, convergence free and so on. In this work, concerted effort has been made to generalize some existing sequence spaces by extending their definitions to a wider space in which the existing ones are contained.