Some geometric properties of certain meromorphically multivalent functions associated with the first-order differential subordination

Abstract

A new subclass $\mathcal{G}_n(A,B,\lambda)$ of meromorphically multivalent functions defined by the first-order differential subordination is introduced. Some geometric properties of this new subclass are investigated. The sharp upper bound on $|z|=r<1$ for the functional $\mathrm{Re}\{(1-\lambda)z^pf(z)-\frac{\lambda}{p}z^{p+1}f'(z)\}$ over the class $\mathcal{G}_n(A,B,0)$ is obtained.

Keywords

• analytic function
• meromorphically multivalent function
• differential subordination
• coefficient estimate
• sharp bound