期刊名称:International Journal of Mathematics and Mathematical Sciences
印刷版ISSN:0161-1712
电子版ISSN:1687-0425
出版年度:1984
卷号:7
DOI:10.1155/S0161171284000478
出版社:Hindawi Publishing Corporation
摘要:Using convolutions, a new family of analytic functions is introduced. This family, called a*-family, serves in certain situations to unify the study of many previously well known classes of analytic functions like multivalent convex, starlike, close-to-convex or prestarlike functions, functions starlike with respect to symmetric points and other such classes related to the class of univalent or multivalent functions. A necessary and sufficient condition on the Taylor series coefficients so that an analytic function with negative coefficients is in an a*-family is obtained and sharp coefficents bound for functions in such a family is deduced. The extreme points of an a*-family of functions with negative coefficients are completely determined. Finally, it is shown that Zmorvic conjecture is true if the concerned families consist of functions with negative coefficients.