부산대학교 도서관

For α,γ ≥ 0, 0 ≤ β < 1 and k ≥ 1, we introduce the functions class RHk(α,γ,β)R(α,γ,β)RHk(α,γ,β)DRHk(α,γ,β)RHk(α,γ,β)WH0(α,β), which is the harmonic analogue to the family RHk(α,γ,β)R(α,γ,β)RHk(α,γ,β)DRHk(α,γ,β)RHk(α,γ,β)WH0(α,β) due to Ali et al. (Complex Var. Elliptic Equ. 58, 1569–1590, 2013). It is observed that the family RHk(α,γ,β)R(α,γ,β)RHk(α,γ,β)DRHk(α,γ,β)RHk(α,γ,β)WH0(α,β) is close-to-convex in RHk(α,γ,β)R(α,γ,β)RHk(α,γ,β)DRHk(α,γ,β)RHk(α,γ,β)WH0(α,β). We first determine the sharp bounds on harmonic Bieberbach-type conjecture, sufficient condition and growth theorems of functions in the family RHk(α,γ,β)R(α,γ,β)RHk(α,γ,β)DRHk(α,γ,β)RHk(α,γ,β)WH0(α,β). It is proved that the family is invariant under the convex combination and convolution. Various radii related problems on the partial sums of f in the class RHk(α,γ,β)R(α,γ,β)RHk(α,γ,β)DRHk(α,γ,β)RHk(α,γ,β)WH0(α,β) are also presented. Other results include radii of convexity and starlikeness of the functions in the class RHk(α,γ,β)R(α,γ,β)RHk(α,γ,β)DRHk(α,γ,β)RHk(α,γ,β)WH0(α,β).