Conic regions and k-uniform convexity

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:105

Article

Kanas, S ; Wisniowska, A

关键词: convex function;    uniformly convex function;    k-uniformly convex function;    Jacobian elliptic function;   

DOI  :  10.1016/S0377-0427(99)00018-7

来源: Elsevier

【 摘 要 】

Let Omega(k) subset of C denote a domain, such that 1 is an element of Omega(k) and partial derivative Omega(k) is a conic section, with eccentricity equal to 1/k. In this paper authors introduce the class of k-uniformly convex functions k-UCV, with the property that the values of the expression 1 + zf (z)/f'(z) lie inside the domain Omega(k). Necessary and sufficient conditions for membership in k-UCV, as well as sharp growth and distortion theorems for k-uniformly convex functions are given. The obtained results generalize the concept of uniform convexity due to A.W. Goodman (Ann. Polon. Math. 56 (1991) 87-92). (C) 1999 Elsevier Science B.V. All rights reserved.

【 授权许可】

Free