Approximation by Micchelli Combination of Half Bernstein Polynomials

This paper improves the rate of convergence of the half Bernstein polynomial of positive and linear operators H n,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 H n,2k (g; x).Lastly, we contrast the repeated combination's outcomes with the numerical outcomes obtained from the sequence H n,2k (g; x) without iterative combination.