PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.) Vol. 35(49), pp. 5360 (1984) 

ON A NEW SUBCLASS OF ANALYTIC $P$VALENT FUNCTIONSShigeyoshi OwaDepartment of Mathematics, Kinki University, Osaka, JapanAbstract: There are many classes of analytic and $p$valent functions in the unit disk U.N.S. Sohi studied a class $S_p(\alpha)$ of analytic and $p$valent functions $$ f(z)= z^p+ \sum_{n=1}^\infty a_{p+n}z^{p+n},\qquad (p\in N) $$ in the unit disk $U$ satisfying the condition $$ f'(z)/pz^{p1}\alpha<\alpha,\qquad (z\in U) $$ for $\alpha >1/2$. In this paper, we consider a new subclass $S_{p,k}(\alpha)$ of analytic and $p$valent functions $$ f(z)= z^p+\sum a_{p+n}z^{p+n},\qquad (p\in N) $$ in the unit disk $U$ satisfying the condition $$ \left\frac{\Gamma(p+1k)D^k_z(z)}{\Gamma(p+1)z^{pk}}\right<\alpha, \qquad (z\in U) $$ for $0 Classification (MSC2000): 26A24 Full text of the article:
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