On new classes of analytic functions with negative coefficients
The author considers the class \(K^*_ n\), \(n\in {\mathbb{N}}\cup \{0\}\), consisting of functions f(z) which satisfy in the unit disc \(| z| <1\), the conditions: \[ 1)\quad f(z)=z-\sum^{\infty}_{k=2}a_ kz^ k,\quad a_ k\geq 0,\quad and \] \[ 2)\quad Re\{D^{n+1} f(z)/D^ n f(z)\}>,\quad where\quad D^ n f(z)=f(z)*(z/(1-z)^{n+1}), \] (*) is the Hadamard product of power series. Coefficient inequalities, distortion and closure results are obtained.
scientific article; zbMATH DE number 3931339