Pre-Schwarzian and Schwarzian norm Estimates for class of Ozaki Close-to-Convex functions

Molla Basir Ahamed; Rajesh Hossain

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arXiv · 2412.18284

Pre-Schwarzian and Schwarzian norm Estimates for class of Ozaki Close-to-Convex functions

Molla Basir Ahamed·Rajesh Hossain

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Abstract

The primary objective of this paper is to derive sharp bounds for the norms of the Schwarzian and pre-Schwarzian derivatives in the Ozaki close-to-convex functions $f$, expressed in terms of their value $f^{\prime\prime}(0)$, in particular, when the quantity is equal to zero. Additionally, we obtain sharp bounds for distortion and growth theorems. We will also derive the sharp bound of pre-Schwarzian norm for a certain class of harmonic mappings whose analytic part is fixed.

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Molla Basir Ahamed, Rajesh Hossain. 2024-12-24. Pre-Schwarzian and Schwarzian norm Estimates for class of Ozaki Close-to-Convex functions. https://arxiv.org/abs/2412.18284

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