Statistical extension of bounded sequence space

Abstract

In this paper by using natural density real valued bounded sequence space l1 is extented and statistical bounded sequence space l st 1 is obtained. Besides the main properties of the space l st 1 , it is shown that l st 1 is a Banach space with a norm produced with the help of density. Also, it is shown that there is no matrix extension of the space l1 that its bounded sequences space covers l st 1 . Finally, it is shown that the space l1 is a non-porous subset of l st 1 .

Statistical extension some types of symmetrically continuity

“…Let an arbitrary element s 1 ∈ T 1 . Considering (1.2) there exists s 2 ∈ T 2 satisfying s 2 > s 1 and for all n ≥ s 2 we have T2(n) n > 1 2 . Further, according to (1.2) there exists s 3 ∈ T 3 with s 3 > s 2 , such that for all n ≥ s 3 , we have…”

“…In [9], Fridy gave specific results on statistical convergence. Last ten decades, in literature there are several studies in different directions on statistical convergence [1,3,5,7,10,14,16,17,26].…”

CERTAIN ASPECTS OF Xrst(G)-CONVERGENCE OF SEQUENCES IN GRADUAL NORMED LINEAR SPACES

“…Later on, statistical convergence was further investigated and worked from the sequence space point of view by Fridy [24,25], Šalát [34], Tripathy [37,38], Connor [16], and many others [3,4,5,6,26].…”