Deferred weighted 𝒜-statistical convergence based upon the (<i>p</i>,<i>q</i>)-Lagrange polynomials and its applications to approximation theorems
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
Abstract Recently, the notion of positive linear operators by means of basic (or q -) Lagrange polynomials and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"><m:mi>𝒜</m:mi></m:math> {\mathcal{A}} -statistical convergence was introduced and studied in [M. Mursaleen, A. Khan, H. M. Srivastava and K. S. Nisar, Operators constructed by means of q -Lagrange polynomials and A -statistical approximation, Appl. Math. Comput. 219 2013, 12, 6911–6918]. In our present investigation, we introduce a certain deferred weighted <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"><m:mi>𝒜</m:mi></m:math> {\mathcal{A}} -statistical convergence in order to establish some Korovkin-type approximation theorems associated with the functions 1, t and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"><m:msup><m:mi>t</m:mi><m:mn>2</m:mn></m:msup></m:math> {t^{2}} defined on a Banach space <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"><m:mrow><m:mi>C</m:mi><m:mo></m:mo><m:mrow><m:mo>[</m:mo><m:mn>0</m:mn><m:mo>,</m:mo><m:mn>1</m:mn><m:mo>]</m:mo></m:mrow></m:mrow></m:math> {C[0,1]} for a sequence of (presumably new) positive linear operators based upon <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"><m:mrow><m:mo>(</m:mo><m:mi>p</m:mi><m:mo>,</m:mo><m:mi>q</m:mi><m:mo>)</m:mo></m:mrow></m:math> {(p,q)} -Lagrange polynomials. Furthermore, we investigate the deferred weighted <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"><m:mi>𝒜</m:mi></m:math> {\mathcal{A}} -statistical rates for the same set of functions with the help of the modulus of continuity and the elements of the Lipschitz class. We also consider a number of interesting special cases and illustrative examples in support of our definitions and of the results which are presented in this paper.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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