New type of generalized difference sequence space of non-absolute type and some matrix transformations

Abstract

In the present paper, we introduce a new difference sequence space rqB(u,p) by using the Riesz mean and the B-difference matrix. We show rqB(u,p) is a complete linear metric space and is linearly isomorphic to the space l(p). We have also computed its ?-, ?- and ?-duals. Furthermore, we have constructed the basis of rqB(u,p) and characterize a matrix class (rqB(u, p), l?).

New structure of Fibonacci numbers using concept of Δ --operator

“…In recent years, some researchers have addressed the approach to constructing a new sequence space by means of the matrix domain of a particular limitation method; see, for instance, [3,4,7,31] and the references therein. In [23], the author has studied the following difference sequence space…”

On some new scenario of Δ-spaces

“…We call a space Y to be FK space if it is a complete metric space with continuous coordinated p r : Y → C where p r (u) = u r for all u ∈ Y and r ∈ N. A normed FK space is called a BK space as defined in [16,23] and etc.…”

Some new approach of spaces of non-integral order

“…Some definitions of non-integral derivatives have been generalized by using techniques of new difference sequence spaces of non-integral order as can be seen in [3,19] etc. To establish a new space with the help of matrix methods were studied by several authors as can be found in [1,[11][12][13][14][15][16][17], [23][24][25][26][27][28][29][30][31]33] and many more. Following the references cited, the scenario here is to put forward and synthesis the spaces R q ( p g , κ) of order κ (non-integral) for which ∆…”