Pre-Schwarzian and Schwarzian norm estimates, growth, and distortion theorems for the generalized Robertson class

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The generalized Robertson class of normalized analytic functions and its subclass can be sharply characterized by pre-Schwarzian derivatives, differential inequalities, and specific growth and distortion theorems. Novelty: ClaimNovelty.INCREMENTAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

Molla Basir Ahamed; Rajesh Hossain

doi:10.1515/ms-2026-0336

August 27, 2026Mathematica Slovaca

Pre-Schwarzian and Schwarzian norm estimates, growth, and distortion theorems for the generalized Robertson class

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Key Points

To establish sharp growth, distortion, and derivative norm bounds for normalized analytic functions belonging to the generalized Robertson class and its subclass.
Analyzed normalized analytic functions on the unit disk using differential subordination conditions.
Applied the Schwarz–Pick lemma to evaluate extremal functions and differential inequalities under the normalization condition where the second derivative at the origin equals zero.
Established sharp characterizations for the restricted Robertson subclass using pre-Schwarzian derivatives and differential inequalities.
Derived explicit extremal functions along with sharp growth and distortion theorems.
Obtained sharp upper norm bounds for both pre-Schwarzian and Schwarzian derivatives.

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Implication

Theoretical study establishes sharp pre-Schwarzian and Schwarzian norm estimates in the generalized Robertson class, highlighting geometric bounds on normalized analytic functions.

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Ahamed et al. (2026) studied this question.

synapsesocial.com/papers/6a92994d8e5d7d1fc0c11192 https://doi.org/10.1515/ms-2026-0336

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Pre-Schwarzian and Schwarzian norm estimates, growth, and distortion theorems for the generalized Robertson class

Key Points

No abstract yet

Implication

Discussion

Cite This Study

Pre-Schwarzian and Schwarzian norm estimates, growth, and distortion theorems for the generalized Robertson class

Key Points

No abstract yet

Implication

Discussion

Cite This Study

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