a*-families of analytic functions
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ID: 167989
1984
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Abstract
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.
| Reference Key |
kapoor1984internationala*-families
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| Authors | ;G. P. Kapoor;A. K. Mishra |
| Journal | structural engineering and mechanics |
| Year | 1984 |
| DOI |
10.1155/S0161171284000478
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| URL | |
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