Vol. 36, No. 3, 1971

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On generalized translated quasi-Cesàro summability

B. T. Y. Kwee

Vol. 36 (1971), No. 3, 731–740
Abstract

Let α > 0,β > 1. The (Ct,α,β) transformation of the sequence {sk} is defined by

     Γ (β +-n-+-2)Γ-(α-+-β +-1)-∞∑--Γ (α-+-k)Γ (k-+-n+-1)--
tn =  Γ (n + 1)Γ (β + 1)Γ (α )    Γ (k+ 1)Γ (α+ β + n+ k + 2)sk,
k=0

and the (Ct,α,β) transformation of the function s(x) is defined by

      Γ (α + β + 1)   ∫ ∞  xα− 1s(x)
g(y) = Γ (α)Γ (β +-1)yβ+1 (x-+-y)α+β+1dx.
0

Some properties of the above two transformations are given in this paper and the relation between the summability methods defined by these transformations is discussed.

Mathematical Subject Classification 2000
Primary: 40G05
Milestones
Received: 1 December 1969
Published: 1 March 1971
Authors
B. T. Y. Kwee