On the relation of Cesàro summability to generalized (Fα,q) summability

Rajagopal, C. T. (1976) On the relation of Cesàro summability to generalized (Fα,q) summability Proceedings of the Indian Academy of Sciences, Section A, 83 (5). pp. 175-187. ISSN 0370-0089

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Standard special cases of the sequence-to-function F (α, q)-transform of Meir admit of a more general, essentially more refined, characterization as the F k (α, q)-transform of the sequel, adapted from one of Faulhaber's. The theorem proved, viz., that (F kα, q) summability for sequences, corresponding to the latter transform, includes Cesáro summability of a positive integer order with a certain rapidity, applies to the standard special cases of (F α, q) and (F k, α, q) summabilities which are, in famiiar notation, summabilities(E υ), (T α), (S β), (V α) and (B α, γ) whose further special case (B1, 1) is Borel summability. The special cases of (V½) and Borel summabilities go back to Hyslop.

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