Coefficient Bounds for Certain Classes of Meromorphic Functions

Abstract

Sharp bounds for |a1−μa02| are derived for certain classes Σ∗(ϕ) and Σα∗(ϕ) of meromorphic functions f(z) defined on the punctured open unit disk for which −zf′(z)/f(z) and (−(1−2α)zf′(z)+αz2f″(z))/((1−α)f(z)−αzf′(z))  (α∈ℂ−(0,1]; ℜ(α)≥0), respectively, lie in a region starlike with respect to 1 and symmetric with respect to the real axis. Also, certain applications of the main results for a class of functions defined through Ruscheweyh derivatives are obtained.