Almost convergence and generalized weighted mean

Abstract

In this paper, we investigate some new sequence spaces which naturally emerge from the concepts of almost convergence and generalized weighted mean. The object of this paper is to introduce to the new sequence spaces obtained as the matrix domain of generalized weighted mean in the spaces of almost null and almost convergent sequences. Furthermore, the beta and gamma dual spaces of the new spaces are determined and some classes of matrix transformations are characterized.

The method of almost convergence with operator of the form fractional order and applications

“…Recently, following the Başar and Kirişci [14], very high quality studies is done(cf. [16], [17], [23], [29], [30], [31], [33], [34], [35], [42], [48]).…”

“…In the book of Basar [13], it can be seen that the qualified studies about matrix domain(also, [4]- [12], [18], [19], [20], [31], [33]- [36]).…”

On A New Almost Convergent Sequence Space Defined By The Matrix ∆_u^λ

“…Therefore, many authors were interested in this subject and by using some known matrices, they did many studies by using some known matrices. Some of them are here: (Başar et al, 2011;Candan, , 2018Candan et al, 2015;Karaisa et al, 2015;Kayaduman et al, 2012a,b;Kirisçi, 2012Kirisçi, , 2014.…”

Integrated and Differentiated Sequence Spaces and Weighted Mean

“…In [22], using the generalized weighted mean, new difference sequence spaces are defined. Kirişci [11] have defined the almost sequence spaces with generalized weighted mean and in [12], studied some properties of new almost sequence spaces derived by generalized weighted mean. Structural properties of the bv space are studied by Cesaro mean, generalized weighted mean and Riesz mean, in [13].…”