A variational method for hyperbolically convex functions
نویسندگان
چکیده
منابع مشابه
A Variational Method for Hyperbolically Convex Functions
In this paper we recall our variational method, based on Julia’s formula for the Hadamard variation, for hyperbolically convex polygons. We use this variational method to prove a general theorem for solving extremal problems for hyperbolically convex functions. Special cases of this theorem provide independent proofs for controlling growth and distortion for hyperbolically convex functions.
متن کاملThree Extremal Problems for Hyperbolically Convex Functions
In this paper we apply a variational method to three extremal problems for hyperbolically convex functions posed by Ma and Minda and Pommerenke [7, 16]. We first consider the problem of extremizing Re f(z) z . We determine the minimal value and give a new proof of the maximal value previously determined by Ma and Minda. We also describe the geometry of the hyperbolically convex functions f(z) =...
متن کاملOn distortion under hyperbolically convex maps
We study the class of hyperbolically convex bounded univalent functions with a boundary normalization in the unit disk U . In the paper we obtain the lower estimate for the distortion in this class. A two-point distortion theorem is also proved. The method of proofs is based on the reduced modulus of digons and the modulus of annuli.
متن کاملA Newton-Like Method for Convex Functions
A Newton-like method for convex functions is derived. It is shown that this method can be better than the Newton method. Especially good results can be obtained if we combine these two methods. Illustrative numerical examples are given. Mathematics Subject Classification: 65H05
متن کاملVariational Gram Functions: Convex Analysis and Optimization
We propose a new class of convex penalty functions, called variational Gram functions (VGFs), that can promote pairwise relations, such as orthogonality, among a set of vectors in a vector space. These functions can serve as regularizers in convex optimization problems arising from hierarchical classification, multitask learning, and estimating vectors with disjoint supports, among other applic...
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: Complex Variables and Elliptic Equations
سال: 2006
ISSN: 1747-6933,1747-6941
DOI: 10.1080/17476930500532624