Some Extremal Problems for Analytic Functions
نویسندگان
چکیده
The paper mainly concerns with functions f , analytic in S : |Imz| < 1 and bounded by a constant M > 1. We state sharp estimates for supR |f ′| under the additional condition supR |f | ≤ 1. Using these estimates we deduce well-known Bernstein’s inequality and some its generalizations for entire functions of a finite type with respect to an arbitrary proximate order. Parallely we investigate also the next extremal problem, related to the mentioned class of functions: if f(ζ) = f(ζ) = 1, for some ζ ∈ S, what is the minimal value of supR |f |? Also we present the description of extremal functions for these problems. 1991 Mathematics Subject Classification: Primary 30A10, 30D15
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تاریخ انتشار 2002