Euler-Ces`aro difference spaces of bounded, convergent and null sequences

Abstract

In this paper, we introduce the spacesl ∞ ,c andc 0 of Euler-Cesàro bounded, convergent and null difference sequences and prove that the inclusions ℓ ∞ ⊂l ∞ , c ⊂c and c 0 ⊂c 0 strictly hold. We show that the spacesc 0 andc turn out to be the separable BK spaces such thatc does not possess any of the following: AK property and monotonicity. We determine the alpha-, beta-and gamma-duals of the new spaces and characterize the matrix classes (c : ℓ ∞ ), (c : c) and (c : c 0 ).

Some Geometric Characterizations of a Fractional Banach Set

“…Taking into account this result and the relations (8), (9), (10) and (11), we have for any n > a 1 Remark 19. Let X be a Banach space, then a non-empty set C X is said to be approximatively compact if for any sequence (x n ) 1 n=1 in C and any y 2 X such that kx n yk !…”

Quasi-Cesàro matrix and associated sequence spaces

“…Several authors have introduced new sequence spaces using the domain of some special triangular matrices. For relevant literature, one may see the papers [2,3,6,7,14,20,23,24,27] and textbooks [4,18,19]. For some recent publications, we refer [16,17,25,26,[30][31][32].…”

On the spaces of Cesàro absolutelyp‐summable, null, and convergent sequences

“…By using matrix domains of special triangle matrices in the classical sequence spaces, many authors have introduced and studied new Banach spaces. For recent developments in this direction, we refer the reader to the articles in previous works 6‐18 and textbooks/monographs 19‐21 and in Mursaleen 22 and Mursaleen and Başar, 23 and the references therein.…”