指数凸函数的增长、畸变与Schwarzian范数估计
Growth, Distortion, and Schwarzian Norm Estimates for Exponentially Convex Functions
- Jadavpur University（贾达普大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文研究指数凸函数类的增长、畸变及Schwarzian范数估计，通过显式Schwarz函数推导参数依赖界，并分析极值问题。
AI中文摘要：
本文研究了指数凸类函数族 \\(\mathcal C_{e^λ}\\)（其中 \\(0<λ\leπ/2\\)，由 \\(1+zf''(z)/f'(z)\prec e^{λz}\\) 定义）中函数的增长、畸变、前Schwarzian范数及Schwarzian范数。通过显式表示相关的Schwarz函数，我们推导了关于 \\(f\\)、\\(f'\\) 及前Schwarzian导数的参数依赖估计。进一步地，在一般归一化条件和附加条件 \\(f''(0)=0\\) 下，我们获得了Schwarzian范数估计。相应的极值问题通过适当的Schwarz函数进行分析，并明确给出了所得界对指数参数的依赖性。
英文摘要：
In this paper, we investigate the growth, distortion, pre-Schwarzian and Schwarzian norms of functions in the exponentially convex class \(\mathcal C_{e^λ}\), \(0<λ\leπ/2\), defined by \(1+zf''(z)/f'(z)\prec e^{λz}\). By representing the associated Schwarz function explicitly, we derive parameter-dependent estimates for \(f\), \(f'\), and the pre-Schwarzian derivative. We further obtain Schwarzian norm estimates under both the general normalization and the additional condition \(f''(0)=0\). The corresponding extremal problems are analyzed through suitable Schwarz functions, and the dependence of the resulting bounds on the exponential parameter is made explicit.
