ON ABSOLUTE FACTORABLE MATRIX SUMMABILITY METHODS

In this paper we give necessary and sufficient conditions for vertical bar C, 0 vertical bar(k) double right arrow vertical bar A(f)vertical bar(s) and vertical bar A(f)vertical bar(k) double right arrow vertical bar C, 0 vertical bar(s) for the case 1 < k <= s < infinity, where vertical bar A(f)vertical bar(k) is absolute factorable summability. So we obtain some known results

Extension of Mazhar's theorem on summability factors

By (X,Y) we denote the set of all sequences such ε that Σanε, is summable Y whenever Σ an is summable , where X and Y are summability methods. In this paper we characterize the set (|C,α|k'|N,pn|) for K >1,α >-1 and arbitrary positive sequences (pn) using functional analytic techniques, and so extend some known results

Representations of functionals on absolute weighted spaces and adjoint operators

In the present paper, we establish general representations of continuous linear functionals, which play important roles in Functional Analysis, of the absolute weighted spaces which have recently been introduced in Sarıgöl (2016, 2011), and also determine their norms. Further making use of this we give adjoint operators of matrix mappings defined on these spaces. Keywords: Sequence spaces, BK spaces, Absolute summability, Continuous linear functiona

Spaces of Series Summable by Absolute Cesaro and Matrix Operators

In this paper giving some algebraic and topological properties of vertical bar C-alpha vertical bar(k), we characterize the classes of all infinite matrices (vertical bar C-alpha vertical bar, vertical bar C-delta vertical bar(k)) and (vertical bar C-alpha vertical bar(k), vertical bar C-delta vertical bar) for alpha, delta > -1 and k >= 1, show that each element of this classes correspond to a continuous linear mapping, which also enables us to extend some well known results of Flett [7], Orhan and Sarigol [15], Bosanquet [2], Mehdi [13], Mazhar [11], and Sarigol [18], where vertical bar C-alpha vertical bar(k) is the space of series summable by absolute Cesaro summability vertical bar C, alpha vertical bar(k) in Flett's notation

Norms and compactness of operators on absolute weighted mean summable series

In a recent paper we characterized the classes of triangular matrix transformations mapping from the spaces |N̄p| and |N̄θ p|k into the spaces |N̄θ q|k and |N̄q|, respectively, where the spaces |N̄θ p|k, k≥1, series summable by absolute summability method. In the present paper we show that each element of these classes corresponds to a bounded linear operator, and determine exactly or estimate their norms and those in some well known classes. Also, we characterize compact operators in these classes by using Hausdorff measure of noncompactness. © 2016, University of Kuwait. All rights reserved

On equivalence of absolute double weighted mean methods

Bor [1], Bor and Thorpe [2] and the author [8] established the set of necessary and sufficient condition for the equivalence of absolute weighted mean summability methods of infinite series. In the present paper we extend their result to doubly infinite series by two dimensional weighted mean, which also includes the result of Rhoades [7]. © 2020, © 2020 NISC (Pty) Ltd

A new series space vertical bar(N)over-bar(p)(theta)vertical bar (mu) and matrix operators with applications

The space vertical bar(N) over bar (theta)(p)vertical bar all series summable by the absolute weighted mean method has recently been introduced and studied in several publications. In the present paper, we define a new notion of generalized absolute summability, which includes several well-known summability methods, and construct a series space vertical bar(N) over bar (theta)(p)vertical bar (mu) corresponding to it. Further, we obtain several properties of the new space and characterize certain matrix transformations on that space. We also deduce some important results as special cases

A new series space |N_p^θ |(μ) and matrix operators with applications

The space |N_p^θ |(μ) all series summable by the absolute weighted mean method has recently been introduced and studied in several publications. In the present paper, we define a new notion of generalized absolute summability, which includes several well-known summability methods, and construct a series space |N_p^θ |(μ) corresponding to it. Further, we obtain several properties of the new space and characterize certain matrix transformations on that space. We also deduce some important results as special cases

Series spaces derived from absolute Fibonacci summability and matrix transformations

In this study we introduce a new series space | Fθ| (p) as the domain of a matrix corresponding to the absolute Fibonacci summability in the Maddox’s space l(p) and show that it is linearly isomorphic to the space l(p) and that it is an FK-space. Also, we determine its duals, base and characterize certain matrix transformations on that space. © 2019, Unione Matematica Italiana