Bregman best proximity points for Bregman asymptotic cyclic contraction mappings in Banach spaces
Bibliographic record
Abstract
In this paper, we first introduce the notion of the BUC property, which extends the notion of UC property introduced and studied in [T.Suzuki, M. Kikawa, C. Vetro, The existence of best proximity points in metric spaces with the property UC, Nonlinear Anal.71 (2009), 2918-2926] for Banach spaces.We then prove, without continuity assumption on mappings, the existence and convergence of Bregman best proximity points for Bregman asymptotic cyclic contractions in Banach spaces with the property BUC and Bregman asymptotic proximal pointwise contractions in uniformly convex Banach spaces.Moreover, we consider a Bregman generalized cyclic contraction mapping and prove the existence of Bregman best proximity points for such a mapping in Banach spaces which do not necessarily satisfy the geometric property BUC.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.008 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.001 | 0.004 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 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 source (direct Gemma or distilled Codex), 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".