Cesàro and Borel-type summability

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.

Transseries and Écalle-Borel summability

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...

On the convergence and Cesàro summability of trigonometric Fourier series of monotone type functions

The behaviour of Cesàro means of trigonometric Fourier series of monotone type functions in the space of continuous functions is studied.

: Existence and Uniqueness of Solutions , Asymptotic and Borel Summability Properties

We consider a system of n-th order nonlinear quasilinear partial differential equations of the form ut + P(∂ j x)u + g ( x, t, {∂ xu} ) = 0; u(x, 0) = uI(x) with u ∈ C, for t ∈ (0, T ) and large |x| in a poly-sector S in C (∂ x ≡ ∂ j1 x1∂ j2 x2 ...∂ jd xd and j1 + ... + jd ≤ n). The principal part of the constant coefficient n-th order differential operator P is subject to a cone condition. The...