Some approximation results for the new modification of Bernstein-Beta operators

This paper deals with the newly modification of Beta-type Bernstein operators, preserving constant and Korovkin's other test functions $e_i=t^i$, $i=1,2$ in limit case. Then the uniform convergence of the constructed operators is given. The rate of convergence is obtained in terms of modulus of continuity, Peetre- $\mathcal{K}$ functionals and Lipschitz class functions. After that, the Voronovskaya-type asymptotic result for these operators is established. At last, the graphical results of the newly defined operators are discussed.