An iterative method for approximating fixed points of Presić nonexpansive mappings
Bibliographic record
Abstract
Some fixed point theorems of Presić type for nonexpansive mappings\(f: X^k\rightarrow X\), where \(k\geq 1\) is an integer, are obtained.The main result of the paper unifies two important fixed point theorems published in the same year, 1965, the first one discovered independently by Browder [F.E. Browder, Nonexpansive nonlinear operators in Banach spaces, Proc. Nat. Acad. Sci. U.S.A., 54 (1965), 1041-1044], Göhde [D. Göhde, Zum Prinzip der kontraktiven Abbildung, Math. Nachr., 30(1965), 251-258] and Kirk [W.A. Kirk, A fixed point theorem for mappings which do not increase distances, Amer. Math. Monthly,72 (1965), 1004-1006], while the second one is due to Presić [S.B. Presić, Sur une classe d' inéquationsaux differences finite et sur la convergence de certaines suites, Publ. Inst. Math. (Beograd)(N.S.), 5(19) (1965),75-78]. In this way we show how amazingly two apparently different beautiful results in mathematics can meet after almost half a century! This appears to be the first attempt to study multi-step iterative methods by means of the fixed point theory of nonexpansive mappings. Several related results in literature are extended, unified and generalized.
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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 | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
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".