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On \((E,1)(C,1)\) summability of Fourier series and its conjugate series. (English) Zbl 1268.42012

Summary: Several researchers like A. N. Singh, S. P. Khare, M. L. Mittal and R. Kumar, U. N. Singh and V. S. Singh, G. S. Pandey and B. L. Jadia have studied \((N,p_{n}),(N,p,q)\), almost \((N,p,q)\) and matrix summability methods for Fourier series and its conjugate series using different conditions. But nothing seems to have been done so far to study \((E,1)(C,1)\) product summability of Fourier series and its conjugate series. Therefore, in this paper, two theorems on \({(E,1)(C,1)}\) summability of Fourier series and its conjugate series under a general condition are proved.

MSC:

42B05 Fourier series and coefficients in several variables
42B08 Summability in several variables