Advanced Mathematical Models & Applications
Advanced Mathematical Models & Applications is a peer-reviewed, open access journal meant to publish original and significant results and articles in all areas of mathematical modeling and their applications. The aim of this Journal is to bring together researchers and practitioners from academia and industry to establishing new collaborations in this area. The Journal will consider for publication also review articles, literature reviews, correspondence concerning views and information published in previous issues.
Approximation by Micchelli Combination of Half Bernstein Polynomials
- Published: 03-08-2025
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This paper improves the rate of convergence of the half Bernstein polynomial of positive and linear operators Hn,2k(g; x) by applying the technique of iterative combination (Micchelli combination). It turns out that this method improves the order of approximations to O(n-k). Next, using this sequence, we investigate the Voronovskaja asymptotic expression in both ordinary and instantaneous approximating for smooth functions. The mistake caused by this approximation is then estimated by means of the modulus for continuity. Next, in order for approximation assessment functions, we provide numerical illustrations via this iterative combination of the sequence Hn,2k(g; x). Lastly, we contrast the repeated combination’s outcomes with the numerical outcomes obtained from the sequence Hn,2k(g; x) without iterative combination.
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