We study problem of (λ, φ) -strong summation of number series by the regular method λ with power summation of the function φ . The accumulated results are extended to the case of Fourier expansions in trigonometric functions f ϵ L p , p > 1 , where C is the set of 2π-periodic continuous functions. Some results are also obtained for the estimation of strong means of the method λ in L p , p > 1 , at the Lebesgue point x of the function f under certain additional conditions in the case where the function φ tends to infinity as u→ ∞ faster than the exponential function exp (βu) − 1, β > 0 .
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 67, No. 6, pp. 809–819, June, 2015.
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Pachulia, N.L. On the Estimation of Strong Means of Fourier Series. Ukr Math J 67, 916–927 (2015). https://doi.org/10.1007/s11253-015-1122-0
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DOI: https://doi.org/10.1007/s11253-015-1122-0