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In this paper, we shall solve a number of extremal problems of which the following two are typical. (a) Let D denote a domain in the complex z-plane which is bounded by n closed analytic curves IF (v=1, , n, F=Il+F2+ * * * +In), and let X(zo) (zoGF) be a positive function which is continuous on each I'. Let further Bx denote the class of analytic functions f(z) which are regular and single-valued in D, vanish at a given point z = of D and, for radial approach from within D, satisfy

A class of domain functions and some allied extremal problems