Certain Geometric Properties and Matrix Transformations on a Newly Introduced Banach Space

Abstract

The main purpose of this study is to characterize some matrix classes from classical sequence spaces into a newly introduced space and find the norm of some special matrix operators. Also, we give certain geometric properties of this space.

On Generalizedp,q-Euler Matrix and Associated Sequence Spaces

“…The ðp, qÞ-Euler matrix B r,t of order ðr, tÞ generalizes some of the well-known matrices presented in the literature, for instance, Binomial matrix B r,t of order ðr, tÞ [39,40], Euler matrix of order r [10,11], etc. Thus, the results presented in this paper strengthen the results of [11,14,40,[52][53][54][55]. As for future scope, we shall study the domain of the matrix B r,t ðp, qÞ in the spaces c and c 0 of convergent and null sequences, respectively.…”

New Banach Sequence Spaces Defined by Jordan Totient Function

“…where ϕ is the Euler totient function. In the recent time, by using this matrix, many new sequence and series spaces are defined and studied in the papers [19][20][21][22][23][24][25][26][27]. For i ∈ N with i = 1, ϕ(i) gives the number of positive integers less than i which are coprime with i and ϕ(1) = 1.…”

Domain of Jordan Totient Matrix in the Space of Almost Convergent Sequences

“…It is a known fact that a convergent sequence is almost convergent such that its ordinary and generalized limits are equal. See the papers [2][3][4][5][6][7][8][9][10][11][12][13][14] for more on almost convergence and Banach limit.…”