Exploring \(\mathfrak{F}\)-Khan-Contraction with Mann's Iterative Scheme in Convex \(S_b\)-Metric Spaces
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Bibliographic record
Abstract
This manuscript presents the concept of Sb metric space for Mann’s iteration scheme, which extends the notion of b-metric, Gb-metric and S-metric spaces, respectively. We begin by introducing some improved and interesting properties, specifically regarding the concepts of symmetric and nonsymmetric within the context of Sb-metric space provided by examples. Additionally, we expand the notation of convex Sb-metric space through a convex Mann’s iteration algorithm. Furthermore, we display numerous outcomes of this new type of notion in the literature, with a particular focus on rational-Khan contractions and Wardowski-type contractions. The aim is to establish fixed-point results, accompanied by examples that clarify our findings. Finally, we provide applications to mixed Volterra-Fredholm integral and polynomial equations to support our theorems.
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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 | 0.001 |
| Bibliometrics | 0.006 | 0.006 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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 it