Abstract
Das (Proc. Camb. Philos. Soc. 67:321-326, 1970) proved that every conservative Hausdorff matrix is absolutely k th power conservative. Savas and Rhoades (Anal. Math. 35:249-256, 2009) proved the result of Das for double Hausdorff summability. In this paper we will consider the double Endl-Jakimovski (E-J) generalization and we will prove the corresponding result of Savas and Sevli (J. Comput. Anal. Appl. 11:702-710, 2009) for double E-J generalized Hausdorff matrices. MSC:40F05, 40G05.
Highlights
Introduction and backgroundThe basic theory of Hausdorff transformations for double sequences was developed by Adams [ ] in
H(α,β) =δ(α,β)μ(α,β)δ(α,β) is called a double E-J generalized Hausdorff matrix corresponding to the sequence (μm(αn,β))
Theorem A matrix H(α,β) = (hm(αn,βij)) is a double E-J generalized Hausdorff matrix corresponding to the sequence (μm(αn,β)) if and only if its elements have the form hm(αn,βij) =
Summary
Introduction and backgroundThe basic theory of Hausdorff transformations for double sequences was developed by Adams [ ] in. Thereafter, Savaş and Rhoades [ ] proved the result of Das [ ] for double Hausdorff summability. In this paper we will consider double E-J generalization and we will prove the corresponding result of [ ] for double E-J generalized Hausdorff matrices. A double Hausdorff matrix has entries m hmnij = i n j m–i n–j μij , where {μij} is any real or complex sequence and m–i m–i n–j n–jμij =
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