On Growth and Approximation of Generalized Biaxially Symmetric Potentials on Parabolic-Convex Sets

Abstract

The regular, real-valued solutions of the second-order elliptic partial differential equationare known as generalized bi-axially symmetric potentials (GBSP's). McCoy [1] has showed that the rate at which approximation error E p 2n 2n (F; D), (p ≥ 2, D is parabolic-convex set) tends to zero depends on the order of GBSP F and obtained a formula for finite order. If GBSP F is an entire function of infinite order then above formula fails to give satisfactory information about the rate of decrease of E p 2n 2n (F; D). The purpose of the present work is to refine above result by using the concept of index-q. Also, the formula corresponding to q-order does not always hold for lower q-order. Therefore we have proved a result for lower q-order also, which have not been studied so far.