Results 221 to 230 of about 5,164 (237)

On absolute riesz and absolute Nörlund summability

Periodica Mathematica Hungarica, 1992
A study of the inclusion problem for \(| N,p|\subset| R,\lambda,k|\), \(k>0\), is taken up and a general theorem involving monotone functions \(p\) and \(\lambda\) is given. This theorem thus provides a counterpart of the theorem for the inclusion \(| R,\lambda,1|\subset| N,p|\) as given in [Indian J. Math. 7, 78-81 (1965; Zbl 0141.249); cf. also Rend.
openaire   +1 more source

Some summability factor theorems for absolute summability

Analysis, 2002
The authors obtain a set of sufficient conditions on methods of summability and on sequences \(\left(e_n\right)\), so that \(\sigma a_n\) summable \(\left|\overline N,p_n\right|_k\) implies \(\sigma a_n e_n\) summable \(\left|T\right|_k\), with \(k\) greater than or equal to 1. As corollaries they obtain the results of \textit{W. T. Sulaiman} [Proc. Am.
Rhoades, B. E., Savaş, Ekrem
openaire   +2 more sources

Some Theorems on Absolute Summability

Canadian Journal of Mathematics, 1951
A summation method defined by the linear transformation will be called an l-l method if ∑|yr| < ∞ whenever ∑|xk| < ∞; if in addition we have ∑yr = ∑xk whenever ∑|xk| < ∞ we shall say the ...
openaire   +1 more source

SOME PROPERTIES OF ABSOLUTE SUMMABILITY DOMAINS

Analysis, 1989
\(\ell\) is the BK-space of sequences \(\{x_ k\}\) with convergent \(\sum | x_ k|\). Given an infinite matrix A, the A-transform of a sequence \(x=\{x_ k\}\) is written as Ax. We write \(\ell_ A=\{x:\) Ax\(\in \ell \}\) and assume \(\ell_ A\supset \phi\), the set of the finite sequences.
Macphail, M. S., Orhan, C.
openaire   +2 more sources

Absolute rate summability domains

Studia Scientiarum Mathematicarum Hungarica, 2004
In this paper we show that for ℓπA, E and E′ are equivalent, and that if either Λ┴πA or IπA is invariant they both are, and then Λ┴πA = IπA = lπA.
openaire   +1 more source

Positivity in Absolute Summability

1987
For the investigation of absolute summability domains we employ two positivity concepts and two kinds of sectional operators. In particular we obtain a basic positivity result for Cesaro methods and subsequently two known results (of Hardy-Bohr type) concerning summability factors.
Wolfgang Beekmann, Karl Zeller
openaire   +1 more source

Absolute Summability Factors

Journal of the London Mathematical Society, 1970
Irwin, R. L., Peterson, G. E.
openaire   +1 more source

Absolute Cesàro summability factors

2002
The author intends to generalize a theorem concerning \(|C,1|_k\) summability factors to \(|C,\alpha, \beta, \delta|_k\) summability using \(\delta\)-quasi-monotone sequences. Unfortunately his Lemma 3 is not correct, consequently the proof of the theorem is not complete. The author will publish a correction soon (personal information).
openaire   +2 more sources

Absolute Summability Factors in a Sequence

Canadian Mathematical Bulletin, 1984
AbstractLet α≥0 and β>— 1. The main result gives necessary and sufficient conditions for the sequence (εn) in order that the sequence (εnUn) will be absolutely summable by the Cesàro method Cβ for each sequence (Un) which is bounded or summable by the method CαAnother theorem is proven when Cα and Cβ are replaced by triangular methods A = (ank) and ...
openaire   +2 more sources

Summability factors for generalized absolute summability. II

Summary: A new theorem concerning the characterization of absolute summability factors has been proved. [For Part I and III see ibid. 31--39 (2001; Zbl 1078.40501) and 47--52 (2001; Zbl 1078.40502).]
openaire   +3 more sources