伯努利双纽线右半区域内两类解析函数的优化问题

Majorization problems for two classes of analytic functions in the right-half of lemniscate of Bernoulli

近些年来,单复变几何函数论中不同区域上解析函数的优化问题备受研究者的关注.本文借助Liu-Owa积分算子和从属关系,分别引入了伯努利双纽线右半区域内一致星象函数类R■(γ,δ)和螺旋函数类S■(a,θ),讨论了其优化问题.所得结果丰富和扩充了单复变几何函数论中的优化理论.

Majorization of analytic functions in different domains has attracted much attention in recent years in the field of geometry function theory of one complex variable. We in this paper introduce the class Rαβ,p(γ,δ) of uniformly starlike functions and the class Sα β,p(a,θ) of spirallike functions in the right-half of lemniscate of Bernoulli, as defined using the Liu-Owa integral operator and subordination relationship, and discuss majorization problems for functions belonging to these classes. Our results so obtained enrich and extend the majorization theory in the field of geometry function theory of one complex variable.