A modification of bernstein polynomals on symmetric range

This work examines the approximation properties and rate of convergence of a modification of Bernstein polynomials on a symmetric interval. The modification of Bernstein polynomials on a symmetric interval is defined as Zד (h, Ψ) = ( ד + 1 2 (ד + 2) ) ד∑ j=0 (ד j ) ( ד + 2 ד + 1 + Ψ )j ( ד + 2 ד + 1 − Ψ )ד−j h (( 2 j ד − 1 ) ד + 2 ד + 1 ) . The approximation properties and rate of convergence of the operator have been studied using its central moments and continuity modulus. Additionally, the approximation of the Zד(h, Ψ) operator in the Lipschitz class has been examined. Finally, the approximation of the operator to certain functions has been demonstrated using numerical value tables that include graphs and error margins.