A New Roper-Suffridge Extension Operator on a Reinhardt Domain

作者：Wang Jianfei^*; Gao Cailing

来源：Abstract and Applied Analysis, 2011, 865496.

DOI：10.1155/2011/865496

We introduce a new Roper-Suffridge extension operator on the following Reinhardt domain Omega(n, p2, ..., pn) = {z is an element of C(n) : |z(1)|(2) + Sigma(n)(j=2)|z(j)|(pj) < 1} given by F(z) = (f(z(1)) + f'(z(1))Sigma(n)(j=2) a(j)z(j)(pj), (f'(z(1)))(1/p2) z(2), ..., (f'(z(1)))(1/p pi) z(n)), where f is a normalized locally biholomorphic function on the unit disc D, p(j) are positive integer, a(j) are complex constants, and j = 2, ..., n. Some conditions for aj are found under which the operator preserves almost starlike mappings of order a and starlike mappings of order a, respectively. In particular, our results reduce to many well-known results when all alpha(j) = 0.

• 出版日期2011
• 单位浙江师范大学