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In the present paper, in order to make the convergence faster to a function being approximated we identify a new generalization of Bernstein operators depending on symmetric range. The rate of convergence of these operators are given by using the modulus of continuity. Furthermore,we establish Korovkin-type approximation theorem and Voronovskaja type asymptotic theorem. Finally, we show that using graphics in Maple this new generalization of Bernstein operators converge faster than Bernstein operators on symmetric range for certain functions.

On approximation properties of a generalization of Bernstein polynomials in symmetric range