A note on extremal properties characterizing weaklyλ-valent principal functions
نویسندگان
چکیده
منابع مشابه
Characterizing sub-topical functions
In this paper, we first give a characterization of sub-topical functions with respect to their lower level sets and epigraph. Next, by using two different classes of elementary functions, we present a characterization of sub-topical functions with respect to their polar functions, and investigate the relation between polar functions and support sets of this class of functions. Finally, we obtai...
متن کاملExtremal properties of rate distortion functions
At a recent workshop (Hakone, Japan, July 1{2, 1988) I. Csiszz ar stated that inspite of strong eeorts the following question had been waiting for an answer for many years. It is true that for xed distortion level the rate{distortion function R(P;) has in the distribution P no local maxima with value diierent from the global maximum? We show that in general the answer is negative. However, the ...
متن کاملExtremal properties of polynomial threshold functions
In this paper we give new extremal bounds on polynomial threshold function (PTF) representations of Boolean functions. Our results include the following: • Almost every Boolean function has PTF degree at most n2 + O( √ n log n). Together with results of Anthony and Alon, this establishes a conjecture of Wang and Williams [32] and Aspnes, Beigel, Furst, and Rudich [4] up to lower order terms. • ...
متن کاملA Note on Radius of Starlikeness and Convexity of p - Valent Analytic Functions
Let Ap denote the class of analytic functions of the form f(z) = z + ∞ ∑ n=p+1 anz n (p ∈ N = {1, 2, 3, ...}) defined in the unit disc U = {z : |z| < 1} and Ω denote the class of functions such that ω(0) = 0 and |ω(z)| < 1. Let P(A,B, p, α) be the class of functions of the form p(z) = p+ ∞ ∑ n=1 anz n and p(z) = p+ γω(z) 1 +Bω(z) , −1 ≤ B < A ≤ 1 where γ = (p−α)A+αB. In this paper, we define th...
متن کاملCharacterizing Properties of Stochastic Objective Functions
This paper develops tools for analyzing properties of stochastic objective functions that take the form ( , ) ( , ) ( ; ) V u dF ≡ ∫s x x s s θ θ . The paper analyzes the relationship between properties of the primitive functions, such as the utility functions u and probability distributions F, and properties of the stochastic objective. The methods are designed to address problems where the ut...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1968
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1968.25.109