To obtain more refined measure of growth the q-pro- ximate type is constructed for a class of generalized biaxially symmetric potentials (GBASP’s). Finally, we obtain lower q-proximate type for GBASP’s. Our results generalize some results of Kumar [7].
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The paper deals with growth and approximation of solutions (not necessarily entire) of certain elliptic partial differential equations. These solutions are called Generalized Bi-Axiaily Symmetric Potentials (GBASP's). The GBASP's are taken to be regular in a finite hyperball and influence of the growth of their maximum moduli on the rate of decay of their approximation errors in sup norm is studied. The author has been obtained the characterizations of the (/-growth number and lower q-growth number of a GBASP &isin H R, O < R < &infin in terms of rate of decay of approximation error En(H, Ro}, 0 < Ro < &infin. Finally we have obtained a necessary condition for a GBASP &isin HR to be of perfectly regular growth.
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Let F(alfa,beta)(x,y) be a real valued regular solution to the generalized biaxially symmetric potential equation (mathematcal formula) To obtain a more refined measure of growth then is given by [1] an approximation theorem for arbitrary proximate types and some more asymptotic properties have been proved. The proximate type is constructed for a class of Generalized Biaxially Symmetric Potential (GBASP). Lastly, we obtain lower and upper bounds for proximate type in reference to growth parameters of GBASP.
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