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  • 标题:<mml:math alttext="$a^* $" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msup><mml:mi>a</mml:mi><mml:mo>*</mml:mo></mml:msup></mml:mrow></mml:math>-families of analytic functions
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  • 作者:G. P. Kapoor ; A. K. Mishra
  • 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.
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