Solving Split Mixed Equilibrium With Multiple Output Sets and Fixed Point of Certain Multi-Valued Mappings
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Bibliographic record
Abstract
In this paper, we study the split mixed equilibrium problem which includes the equilibrium problem, split convex minimization problem and split equilibrium problem, to mention a few. In addition, we propose a Halpern iterative method for solving split mixed equilibrium problem with multiple output sets and fixed point of a finite family of multi-valued strictly pseudo-contractive mappings in the framework of real Hilbert spaces. We prove a strong convergence theorem without imposing any compactness condition. Lastly, we present some consequences and give applications of our main result to split mixed variational inequality and split convex minimization problems. The result discussed in this article extends and complements many related results in literature.
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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 | 0.000 |
| Bibliometrics | 0.002 | 0.002 |
| 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 it