On a class of p-valent starlike functions of order α
Let Ω denote the class of functions w(z), w(0)=0, |w(z)|<1 analytic in the unit disc ⋃={z:|z|<1}. For arbitrary fixed numbers A, B, −1<A≤1, −1≤B<1 and 0≤α<p, denote by P(A,B,p,α) the class of functions p(z)=p+∑n=1∞bnzn analytic in ⋃ such that P(z) ϵ P(A,B,p,α) if and only if P(z)=p+[...
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| Format: | Article |
| Language: | English |
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Wiley
1987-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171287000838 |
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| _version_ | 1832545380036771840 |
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| author | M. K. Aouf |
| author_facet | M. K. Aouf |
| author_sort | M. K. Aouf |
| collection | DOAJ |
| description | Let Ω denote the class of functions w(z), w(0)=0, |w(z)|<1 analytic in the unit disc ⋃={z:|z|<1}. For arbitrary fixed numbers A, B, −1<A≤1, −1≤B<1 and 0≤α<p, denote by P(A,B,p,α) the class of functions p(z)=p+∑n=1∞bnzn analytic in ⋃ such that P(z) ϵ P(A,B,p,α) if and only if P(z)=p+[pB+(A−B)(p−α)]w(z)1+Bw(z), w ϵ Ω, z ϵ ⋃. Moreover, let S(A,B,p,α) denote the class of functions f(z)=zp+∑n=p+1∞anzn analytic in ⋃ and satisfying the condition that f(z) ϵ S(A,B,p,α) if and only if zf′(z)f(z)=P(z) for some P(z) ϵ P(A,B,p,α) and all z in ⋃. In this paper we determine the bounds for |f(z)| and |argf(z)z| in S(A,B,p,α), we investigate the coefficient estimates for functions of the class S(A,B,p,α) and we study some properties of the class S(A,B,p,α). |
| format | Article |
| id | doaj-art-864800da67ef4d51bdb0c5ff459abf32 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1987-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-864800da67ef4d51bdb0c5ff459abf322025-02-03T07:26:01ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251987-01-0110473374410.1155/S0161171287000838On a class of p-valent starlike functions of order αM. K. Aouf0Dept. of Maths., Faculty of Science, University of Mansoura, Mansoura, EgyptLet Ω denote the class of functions w(z), w(0)=0, |w(z)|<1 analytic in the unit disc ⋃={z:|z|<1}. For arbitrary fixed numbers A, B, −1<A≤1, −1≤B<1 and 0≤α<p, denote by P(A,B,p,α) the class of functions p(z)=p+∑n=1∞bnzn analytic in ⋃ such that P(z) ϵ P(A,B,p,α) if and only if P(z)=p+[pB+(A−B)(p−α)]w(z)1+Bw(z), w ϵ Ω, z ϵ ⋃. Moreover, let S(A,B,p,α) denote the class of functions f(z)=zp+∑n=p+1∞anzn analytic in ⋃ and satisfying the condition that f(z) ϵ S(A,B,p,α) if and only if zf′(z)f(z)=P(z) for some P(z) ϵ P(A,B,p,α) and all z in ⋃. In this paper we determine the bounds for |f(z)| and |argf(z)z| in S(A,B,p,α), we investigate the coefficient estimates for functions of the class S(A,B,p,α) and we study some properties of the class S(A,B,p,α).http://dx.doi.org/10.1155/S0161171287000838p-Valentanalyticboundsstarlike functions of order α. |
| spellingShingle | M. K. Aouf On a class of p-valent starlike functions of order α International Journal of Mathematics and Mathematical Sciences p-Valent analytic bounds starlike functions of order α. |
| title | On a class of p-valent starlike functions of order α |
| title_full | On a class of p-valent starlike functions of order α |
| title_fullStr | On a class of p-valent starlike functions of order α |
| title_full_unstemmed | On a class of p-valent starlike functions of order α |
| title_short | On a class of p-valent starlike functions of order α |
| title_sort | on a class of p valent starlike functions of order α |
| topic | p-Valent analytic bounds starlike functions of order α. |
| url | http://dx.doi.org/10.1155/S0161171287000838 |
| work_keys_str_mv | AT mkaouf onaclassofpvalentstarlikefunctionsofordera |