Corrigenda: ``On generalized Cesàro means of integral order''

On generalized absolute Cesàro summability

In this paper, a main theorem dealing with | C, 1 |k summability factors has been generalized under more weaker conditions for | C,α, β |k summability factors. This theorem also includes some new results. Mathematics Subject Classification 2000: 40D15, 40F05, 40G05, 40G99.

On the Approximation Properties of Cesàro Means of Negative Order of Walsh-Fourier Series

In this paper we establish approximate properties of Cesàro (C,−α)-means with α ∈ (0, 1) of Walsh-Fourier series. This result allows one to obtain the condition which is sufficient for the convergence of the means σ−α n (f, x) to f (x) in the L p-metric. We also show that this condition cannot be improved in the case p = 1.

Summability of the l-1 Cesàro means of an integral transformation connected to a Riesz potential

Cesàro means of Jacobi expansions on the parabolic biangle

We study Cesàro (C, δ) means for two-variable Jacobi polynomials on the parabolic biangle B = {(x1, x2) ∈ R2 : 0 ≤ x1 ≤ x2 ≤ 1}. Using the product formula derived by Koornwinder & Schwartz for this polynomial system, the Cesàro operator can be interpreted as a convolution operator. We then show that the Cesàro (C, δ) means of the orthogonal expansion on the biangle are uniformly bounded if δ > ...

Factors for generalized absolute Cesàro summability

A positive sequence (bn) is said to be almost increasing if there exists a positive increasing sequence cn and two positive constants A and B such that Acn ≤ bn ≤ Bcn (see [1]). Obviously every increasing sequence is almost increasing but the converse need not be true as can be seen from the example bn = ne(−1) n . Let ∑ an be a given infinite series with partial sums (sn). We denote by tn n-th...