A sufficient condition for \((F_1)\)-effectiveness of the \(C^1T\)-method
Summability of a class of series consisting of Fourier series and some other related series by \((N,p)\) and \((C,1).(N,p)\) methods have been, respectively, studied by \textit{E. Hille} and \textit{J. D. Tamarkin} [Trans. Am. Math. Soc. 34, 757-783 (1932; Zbl 0005.29102)] and \textit{H. P. Dikshit} [Pac. J. Math. 30, 399-410 (1969; Zbl 0181.34101) and Ann. Math. Pura. Appl., IV. Ser. 94, 11-31 (1972; Zbl 0275.42010)]. A necessary and sufficient condition for the \((C,1).(N,p)\) summability of the foregoing class of series was obtained by \textit{A. Kumar} and \textit{G. V. Prasad} [J. Indian Math. Soc., New Ser. 54, No. 1-4, 139-146 (1989; Zbl 0707.42011)]. The author obtains a set of conditions which are sufficient for \(A.(C,1)\) summability of the above class of series, where \(A\) is a triangular matrix method.
scientific article; zbMATH DE number 1218571