satisfying zZ\ \^A < °°, if and only if f is) is bounded away from zero in the half-plane 0-3:0. This discovery amounts to a determination of the spectrum of the Banach-algebra element associated with fis), and it thus makes available for the theory of ordinary Dirichlet series the well-known theorem of Gelfand on analytic functions of Banach-algebra elements (see §24D of [7]) and its generaliz...

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Recommended by Laszlo Toth Suffcient conditions, necessary conditions for faster convergent infinite series, faster τ-convergent infinite series are studied. The faster convergence of infinite series of Kummer's type is proved. Copyright q 2008 Dušan Hoí y et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distributi...

There are various linear and nonlinear one-dimensional partial differential equations that the focus of this research. a large number these cannot be solved analytically or precisely. The evaluation equations, even if analytical solutions exist, may problematic. Therefore, it necessary to use approximate methodologies solve issues. As result, more effective accurate approach must investigated a...

In this article, a hybrid method that combines Aboodh transform, variational iteration method, and the homotopyperturbation is presented for approximate solution of important partial differential equations describe wave like in one, two three dimensions. The suggested utilizes only initial conditions to providean analytical solution, contrast separation variables, also requires boundary conditi...