A new perspective on paranormed Riesz sequence space of non-absolute type

Abstract

The current article mainly dwells on introducing Riesz sequence space r q ( B . Eventually, we characterize a matrix class on the sequence space. These results are more general and more comprehensive than the corresponding results in the literature.

A different approach for almost sequence spaces defined by a generalized weighted means

“…Further, using generalized difference Fibonacci matrix, Candan and Kayaduman defined ̂ ( , ) space [24]. Furthermore, it can be looked at those works about this topic nearly: [9], [10], [11], [25], [26], [27], [28], [29], [30], [31]…”

“…[20] x) = ( ) ∈ ( : ) necessary and sufficient condition (26) and (29) yield. [21] xi) = ( ) ∈ ( : ) necessary and sufficient condition (27) and (28) yield. [22] xii) = ( ) ∈ ( : ) necessary and sufficient condition (30) and (33) yield.…”

“…Corollary 5: The following statements hold: i) = ( ) ∈ : ( , ) necessary and sufficient condition (20), (26) and (28) ii) = ( ) ∈ : ( , ) necessary and sufficient condition (26) and (29) yield with lieu of . iii) = ( ) ∈ : ( , ) necessary and sufficient condition (27) and (28) yield with lieu of .…”

A new paranormed sequence space defined by Catalan conservative matrix

“…For the literature review, one can refer to previous studies [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] about normed spaces and paranormed spaces derived by domains of special infinite matrices.…”