An inclusion theorem for generalized Lototsky summability methods

1972 ◽  
Vol 25 (1) ◽  
pp. 203-216 ◽  
Author(s):  
H. B. Skerry
Keyword(s):  
Inclusion Theorem ◽  
Summability Methods

scholarly journals A note on an inclusion theorem

2001 ◽  
Vol 32 (1) ◽  
pp. 39-44
Author(s):  
Huseyin Bor
Keyword(s):  
Inclusion Theorem ◽  
Summability Methods

In this paper a relation between the $ | C, \alpha; \delta |_k $ and $ | \bar{N}, p_n; \delta |_k $ summability methods, which generalizes a result of Bor[2] concerning the $ | C, 1|_k $ and $ | \bar{N}, p_n |_k $ summability methods, is proved.

scholarly journals On an inclusion theorem

2000 ◽  
Vol 24 (6) ◽  
pp. 385-388 ◽  
Author(s):  
Hüseyin Bor
Keyword(s):  
Inclusion Theorem ◽  
Summability Methods

We have established a relation betweenθ−|R,pn|kandθ−|R,qn|ksummability methods,k>1, which generalizes a result of Sunouchi (1949) on|R,pn|and|R,qn|summability methods.

scholarly journals COMPARISON OF SPEEDS OF CONVERGENCE IN RIESZ‐TYPE FAMILIES OF SUMMABILITY METHODS. II

2010 ◽  
Vol 15 (1) ◽  
pp. 103-112 ◽  
Author(s):  
Anna Šeletski ◽  
Anne Tali
Keyword(s):  
Tauberian Theorem ◽  
Inclusion Theorem ◽  
Numerical Examples ◽  
Summability Methods ◽  
The Family

Certain summability methods for functions and sequences are compared by their speeds of convergence. The authors are extending their results published in paper [9] for Riesz‐type families {Aα} (α > α0 ) of summability methods Aα . Note that a typical Riesz‐type family is the family formed by Riesz methods Aα = (R, α), α > 0. In [9] the comparative estimates for speeds of convergence for two methods Aγ and Aβ in a Riesz‐type family {Aα}were proved on the base of an inclusion theorem. In the present paper these estimates are improved by comparing speeds of three methods Aγ, Aβ and Aδ on the base of a Tauberian theorem. As a result, a Tauberian remainder theorem is proved. Numerical examples given in [9] are extended to the present paper as applications of the Tauberian remainder theorem proved here.

scholarly journals On Dirichlet convolution method

1998 ◽  
Vol 21 (3) ◽  
pp. 607-611
Author(s):  
Indulata Sukla
Keyword(s):  
Summability Methods ◽  
Dirichlet Convolution ◽  
Convolution Method

In this paper we have proved limitation theorem for(D,h(n))summability methods and have shown that it is best possible.

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