Results 21 to 30 of about 39 (39)
Topological duals of some paranormed sequence spaces
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 30, Page 1883-1897, 2003., 2003 Let P = (pk) be a bounded positive sequence and let A = (ank) be an infinite matrix with all ank ≥ 0. For normed spaces E and Ek, the matrix A generates the paranormed sequence spaces [A, P] ∞((Ek)), [A, P] 0((Ek)), and [A, P]((E)), which generalise almost all the well‐known sequence spaces such as c0, c, lp, l∞, and wp.
Nandita Rath
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Some sequence spaces and statistical convergence
International Journal of Mathematics and Mathematical Sciences, Volume 29, Issue 5, Page 303-306, 2002., 2002 We introduce the strongly (V, λ)‐convergent sequences and give the relation between strongly (V, λ)‐convergence and strongly (V, λ)‐convergence with respect to a modulus.
E. Savaş
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Rate preservation of double sequences under l‐l type transformation
International Journal of Mathematics and Mathematical Sciences, Volume 30, Issue 10, Page 637-643, 2002., 2002 Following the concepts of divergent rate preservation for ordinary sequences, we present a notion of rates preservation of divergent double sequences under l‐l type transformations. Definitions for Pringsheim limit inferior and superior are also presented.
Richard F. Patterson
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Analogues of some Tauberian theorems for stretchings
International Journal of Mathematics and Mathematical Sciences, Volume 27, Issue 2, Page 99-109, 2001., 2001 We investigate the effect of four‐dimensional matrix transformation on new classes of double sequences. Stretchings of a double sequence is defined, and this definition is used to present a four‐dimensional analogue of D. Dawson′s copy theorem for stretching of a double sequence. In addition, the multidimensional analogue of D. Dawson′s copy theorem is
Richard F. Patterson
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Vector‐valued sequence spaces generated by infinite matrices
International Journal of Mathematics and Mathematical Sciences, Volume 26, Issue 9, Page 547-560, 2001., 2001 Let A = (ank) be an infinite matrix with all ank ≥ 0 and P a bounded, positive real sequence. For normed spaces E and Ek the matrix A generates paranormed sequence spaces such as [A,P]∞((Ek)), [A,P]0((Ek)), and [A, P](E) which generalize almost all the existing sequence spaces, such as l∞, c0, c, lp, wp, and several others.
Nandita Rath
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Quadratic Approximation of Generalized Tribonacci Sequences
Discussiones Mathematicae - General Algebra and Applications, 2018 In this paper, we give quadratic approximation of generalized Tribonacci sequence {Vn}n≥0 defined by Vn = rVn−1 + sV n−2 + tV n−3 (n ≥ 3) and use this result to give the matrix form of the n-th power of a companion matrix of {Vn}n≥0. Then we re-prove the
Cerda-Morales Gamaliel
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International Journal of Mathematics and Mathematical Sciences, Volume 27, Issue 7, Page 399-406, 2001., 2001 We prove necessary and sufficient Tauberian conditions for sequences summable by weighted mean methods. The main results of this paper apply to all weighted mean methods and unify the results known in the literature for particular methods. Among others, the conditions in our theorems are easy consequences of the slowly decreasing condition for real ...
Ferenc Móricz, Ulrich Stadtmüller
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Matrix transformations of starshaped sequences
International Journal of Mathematics and Mathematical Sciences, Volume 28, Issue 4, Page 189-200, 2001., 2001 We deal with matrix transformations preserving the starshape of sequences. The main result gives the necessary and sufficient conditions for a lower triangular matrix A to preserve the starshape of sequences. Also, we discuss the nature of the mappings of starshaped sequences by some classical matrices.
Chikkanna R. Selvaraj, Suguna Selvaraj
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Noninclusion theorems: some remarks on a paper by J. A. Fridy
International Journal of Mathematics and Mathematical Sciences, Volume 23, Issue 2, Page 119-122, 2000., 2000 In 1997, J. A. Fridy gave conditions for noninclusion of ordinary and of absolute summability domains. In the present note, these conditions are interpreted in a natural topological context thus giving new proofs and also explaining why one of these conditions is too weak. Also an open question posed in Fridy′s paper is answered.
W. Beekmann
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Lacunary statistical convergence and inclusion properties between lacunary methods
International Journal of Mathematics and Mathematical Sciences, Volume 23, Issue 3, Page 175-180, 2000., 2000 A lacunary sequence is an increasing integer sequence θ = {kr} such that kr − kr−1 → ∞ as r → ∞. A sequence x is called sθ‐convergent to L provided that for each ϵ > 0, limr(1/(kr − kr−1)){the number of kr−1 < k ≤ kr : |xk − L| ≥ ϵ} = 0. In this paper, we study the general description of inclusion between two arbitrary lacunary sequences convergent.
Jinlu Li
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