A class of multivalent functions with negative coefficients defined by convolution

摘要

For a given $p$-valent analytic function $g$ with positivecoefficients in the open unit disk $UD$, we study a class offunctions $f(z)=z^p-sum_{n=m}^infty a_nz^n$ ($a_ngeq 0$) satisfying [ rac{1}{p}Re left( rac{z(f*g)'(z)}{(f*g)(z)}ight) > lphaquad (0leq lpha<1; zinDelta).]Coefficient inequalities, distortion and covering theorems, aswell as closure theorems are determined. The results obtainedextend several known results as special cases.