Abstract
We have generalized Littlewood Tauberian theorems for(C,k,r)summability of double sequences by using oscillating behavior and de la Vallée-Poussin mean. Further, the generalization of(C,r)summability from(C,k,r)summability is given as corollaries which were earlier established by the authors.
Highlights
Let u = be a double real sequence
The de la Vallee-Poussin mean of double real sequence is defined by τmn (u)
For k ≠ 0 and r = 0, (C, k, r) summability reduces to (C, k, 0) summability and the following corollaries are generated from the main result
Summary
Let u = (umn) be a double real sequence. We say that a double sequence u = (umn) is (C, 1, 1) summable to s if σm(1n1)(u) converges to s, as m, n → ∞. A double sequence u = (umn) is said to be (C, k, r) summable to s if σm(knr)(u) converges to s.
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