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Fekete-Szego problem for close-to-convex functions with respect to a certain convex function dependent on a real parameter

Fekete-Szego problem for close-to-convex functions with respect to a certain convex function dependent on a real parameter
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摘要 Given α∈[0, 1], let hα(z) := z/(1 - αz), z ∈ D := {z ∈ C: |z| 〈 1}. An analytic standardly normalized function f in D is called close-to-convex with respect to hα if there exists δ ∈ (-π/2, π/2) such that Re{e^iδ zf′(z)/hα(z)} 〉 0, z ∈ D. For the class l(hα) of all close-to-convex functions with respect to hα, the Fekete-Szego problem is studied. Given α∈[0, 1], let hα(z) := z/(1 - αz), z ∈ D := {z ∈ C: |z| 〈 1}. An analytic standardly normalized function f in D is called close-to-convex with respect to hα if there exists δ ∈ (-π/2, π/2) such that Re{e^iδ zf′(z)/hα(z)} 〉 0, z ∈ D. For the class l(hα) of all close-to-convex functions with respect to hα, the Fekete-Szego problem is studied.
出处 《Frontiers of Mathematics in China》 SCIE CSCD 2016年第6期1471-1500,共30页 中国高等学校学术文摘·数学(英文)
关键词 Fekete-Szego problem close-to-convex functions close-to-convex functions with argument δ close-to-convex functions with respect to a convex function functions of bounded turning Fekete-Szego problem, close-to-convex functions, close-to-convex functions with argument δ, close-to-convex functions with respect to a convex function, functions of bounded turning
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