In this work, we define new sequence spaces by combining generalized weighted mean and difference operator. Afterward, we investigate topological structure which are completeness, AK-property, AD-property. Also, we compute the α− , β− and γ− duals, and obtain bases for these sequence spaces. Finally, necessary and sufficient conditions on an infinite matrix belonging to the classes (c (u, v, ∆) : ℓ∞) and (c (u, v, ∆) : c) are established.2000 Mathematics Subject Classification. 46A05, 46A35, 46A45. Key words and phrases. Difference sequence space, generalized weighted mean, AK and AD properties, the α−, β− and γ− duals and bases of sequences, matrix mappings.
In this paper, we first define a new regular matrix by using the arithmetic function called Jordan totient function and study the matrix domain of this newly introduced matrix in the Banach space ℓp. After computing the dual spaces of this new space, we characterize certain matrix mappings related to this space.
The purpose of this work is to investigate types of convergence of sequences of functions in intuitionistic fuzzy normed spaces and some properties related with these concepts.
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