a*-families of analytic functions
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 star...
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| Format: | Article |
| Language: | English |
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Wiley
1984-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171284000478 |
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| _version_ | 1832556291193569280 |
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| author | G. P. Kapoor A. K. Mishra |
| author_facet | G. P. Kapoor A. K. Mishra |
| author_sort | G. P. Kapoor |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-b01c6cba7ff344eaac458fce8d1d4940 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1984-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-b01c6cba7ff344eaac458fce8d1d49402025-02-03T05:45:53ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251984-01-017343544210.1155/S0161171284000478a*-families of analytic functionsG. P. Kapoor0A. K. Mishra1Department of Mathematics, Indian Institute of Technology, Kanpur 208016, U.P., IndiaDepartment of Mathematics, Indian Institute of Technology, Kanpur 208016, U.P., IndiaUsing 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.http://dx.doi.org/10.1155/S0161171284000478univalent functionsmultivalent functionsconvolutionp-valent starlike functionsp-valent close-to-convex functionsp-valent prestarlike funationsstarlike functions with respect to symmetric pointscoefficients boundextreme points etc. |
| spellingShingle | G. P. Kapoor A. K. Mishra a*-families of analytic functions International Journal of Mathematics and Mathematical Sciences univalent functions multivalent functions convolution p-valent starlike functions p-valent close-to-convex functions p-valent prestarlike funations starlike functions with respect to symmetric points coefficients bound extreme points etc. |
| title | a*-families of analytic functions |
| title_full | a*-families of analytic functions |
| title_fullStr | a*-families of analytic functions |
| title_full_unstemmed | a*-families of analytic functions |
| title_short | a*-families of analytic functions |
| title_sort | a families of analytic functions |
| topic | univalent functions multivalent functions convolution p-valent starlike functions p-valent close-to-convex functions p-valent prestarlike funations starlike functions with respect to symmetric points coefficients bound extreme points etc. |
| url | http://dx.doi.org/10.1155/S0161171284000478 |
| work_keys_str_mv | AT gpkapoor afamiliesofanalyticfunctions AT akmishra afamiliesofanalyticfunctions |