Nörlund Means and Almost Convergence

1978 ◽  
Vol s2-17 (2) ◽  
pp. 317-320
Author(s):  
I. J. Maddox
Keyword(s):  
Almost Convergence ◽  
Nörlund Means

On functional Nörlund methods

1970 ◽  
Vol 67 (1) ◽  
pp. 47-60 ◽  
Author(s):  
B. Choudhary
Keyword(s):  
The Other ◽  
Integral Transformations ◽  
Other Hand ◽  
Nörlund Means ◽  
The One ◽  
Image Position

Integral transformations analogous to the Nörlund means have been introduced and investigated by Kuttner, Knopp and Vanderburg(6), (5), (4). It is known that with any regular Nörlund mean (N, p) there is associated a functionregular for |z| < 1, and if we have two Nörlund means (N, p) and (N, r), where (N, pr is regular, while the function is regular for |z| ≤ 1 and different) from zero at z = 1, then q(z) = r(z)p(z) belongs to a regular Nörlund mean (N, q). Concerning Nörlund means Peyerimhoff(7) and Miesner (3) have recently obtained the relation between the convergence fields of the Nörlund means (N, p) and (N, r) on the one hand and the convergence field of the Nörlund mean (N, q) on the other hand.

scholarly journals Advances in almost convergence

2012 ◽  
Vol 3 (1) ◽  
pp. 49-66
Author(s):  
Chao You
Keyword(s):  
Almost Convergence

Uniform summability of power series

1972 ◽  
Vol 71 (2) ◽  
pp. 335-341 ◽  
Author(s):  
J. C. Kurtz ◽  
W. T. Sledd
Keyword(s):  
Banach Space ◽  
Power Series ◽  
Normal Matrix ◽  
Cesàro Means ◽  
Summability Factors ◽  
Cesaro Means ◽  
Space Topology ◽  
Nörlund Means ◽  
Summability Field ◽  
Cesáro Means

AbstractIt is shown that for the Cesàro means (C, α) with α > - 1, and for a certain class of more general Nörlund means, summability of the series σan implies uniform summability of the series σan zn in a Stolz angle at z = 1.If B is a normal matrix and (B) denotes the series summability field with the usual Banach space topology, then the vectors {ek} (ek = {0,0,..., 1,0,...}) are said to form a Toplitz basis for (B) relative to a method H if H — Σakek = a for each a = {ak}ε(B). It is shown for example that the above relation holds for B = (C,α), α> − 1 , and H = Abel method; also for B = (C,α) and H = (C,β) with 0 ≤ α ≤ β.Applications are made to theorems on summability factors.

Absolute Almost Convergence

2021 ◽  
pp. 89-102
Author(s):  
Gokulananda Das ◽  
Sudarsan Nanda
Keyword(s):  
Almost Convergence
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