We give a criterion for a real-analytic function defined on a compact nonsingular real algebraic set to be analytically equivalent to a rational function.
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The object of the present paper is to derive some inequalities involving multivalent functions in the unit disk. One of our results is an improvement and a generalization of a result due to R. M. Robinson [4].
CONTENTS Introduction..............................................................................5 1. Preliminaries........................................................................5 2. Spaces of smooth elements.................................................8 3. Spaces of D-analytic elements...........................................21 4. Spaces of D-paraanalytic elements....................................32 5. Characterization of .D-paraanalytic elements by means of property (c) and canonical mappings.............39 6. D-R paraanalytic functions .................................................47 7. Smooth elements in Leibniz D-algebras..............................59 8. Weak E-solutions................................................................63 9. Linear systems with scalar coefficients...............................79 10. Linear boundary value problems .....................................82 References.............................................................................97
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Let f(z), $z = re^{iθ}$, be analytic in the finite disc |z| < R. The growth properties of f(z) are studied using the mean values $I_δ(r)$ and the iterated mean values $N_{δ,k}(r)$ of f(z). A convexity result for the above mean values is obtained and their relative growth is studied using the order and type of f(z).
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