Slow Growth and Optimal Approximation of Pseudoanalytic Functions on the Disk

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Devendra Kumar, Slow Growth and Optimal Approximation of Pseudoanalytic Functions on the Disk, Int. J. Anal. Appl., 2 (1) (2013), 26-37.

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Devendra Kumar

Abstract

Pseudoanalytic functions (PAF) are constructed as complex combination of real-valued analytic solutions to the Stokes-Betrami System. These solutions include the generalized biaxisymmetric potentials. McCoy [10] considered the approximation of pseudoanalytic functions on the disk. Kumar et al. [9] studied the generalized order and generalized type of PAF in terms of the Fourier coefficients occurring in its local expansion and optimal approximation errors in Bernstein sense on the disk. The aim of this paper is to improve the results of McCoy [10] and Kumar et al. [9]. Our results apply satisfactorily for slow growth.

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