A Viscosity Approximation Method for Solving General System of Variational Inequalities, Generalized Mixed Equilibrium Problems and Fixed Point Problems
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Bibliographic record
Abstract
This paper is devoted to introducing a new viscosity approximation method using the implicit midpoint rules for finding a common element in the set of solutions of a generalized mixed equilibrium problem, the set of solutions of a general system of variational inequalities and the set of common fixed points of a finite family of nonexpansive mappings in a symmetric Hilbert space. Then, we prove a strong convergence theorem regarding the proposed iterative scheme under some suitable conditions on the parameters. Finally, we provide two numerical results to show the consistency and accuracy of the scheme. One of them, moreover, compares the behavior of our scheme with the iterative scheme of Ke and Ma (Fixed Point Theory Appl 190, 2015).
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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 | 0.002 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 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