Strong Convergence of Cesàro Mean Sequences and Split Equilibrium Solutions via Hybrid Mappings in Hilbert Spaces
Bibliographic record
Abstract
This paper introduces a novel accelerated shrinking projection algorithm for approximating Cesàro mean sequences and solving split equilibrium problems in real Hilbert spaces. The iterative scheme is constructed using finite families of commutative, normally m-generalized hybrid mappings, with a step size chosen independently of the spectral radius to facilitate computation. We prove that the generated sequence converges strongly to a common element in the intersection of the fixed point sets of the mappings, which also solves the associated split equilibrium problem. The proposed method yields new and extended strong convergence theorems for various classes of hybrid mappings, including normally generalized hybrid, m-generalized hybrid, and normally 2-generalized hybrid mappings. A numerical example is provided to demonstrate the superior convergence rate of our algorithm compared to existing methods. These results generalize and unify several known findings in this direction.
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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 | 0.002 | 0.003 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| 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".