A Study of Bi-Univalent Class in Leaf-Like Domains Using Quantum Calculus Through Subordination
Bibliographic record
Abstract
In this work, we introduce and study a new subclass of bi-univalent analytic functions that are associated with a leaf-shaped region, formulated through the framework of q-calculus and the principle of subordination. employing appropriate analytical techniques, we derive sharp coefficient estimates with a particular focus on the initial bounds for |a2| and |a3|, which play a central role in geometric function theory. In addition, we establish Fekete–Szegö-type inequalities for functions belonging to the proposed class, thereby extending and complementing several existing results in the literature. To illustrate the theoretical findings, we provide explicit examples and graphical representations that highlight the behavior of functions in the class under consideration. The analysis not only broadens the applicability of q-calculus methods in the study of bi-univalent functions but also contributes to a deeper understanding of function classes connected with geometrically significant domains. Potential avenues for further research and connections to related subclasses are also discussed.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.003 | 0.005 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".