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arXiv · 2609.27563

Growth, Distortion, and Schwarzian Norm Estimates for Exponentially Convex Functions

Molla Basir Ahamed·Rajesh Hossain
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Abstract

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.

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Molla Basir Ahamed, Rajesh Hossain. 2026-09-23. Growth, Distortion, and Schwarzian Norm Estimates for Exponentially Convex Functions. https://arxiv.org/abs/2609.27563

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