On Kantorovich Modification of (p, q)-Bernstein Operators

Mohiuddine, S. A./0000-0002-9050-9104; Acar, Tuncer/0000-0003-0982-9459WOS: 000440738200050In the present paper, we introduce Kantorovich modifications of (p, q)-Bernstein operators using a new (p, q) -integral. We first estimate the moments and central moments. We obtain uniform convergence of new operators, rate of convergence in terms of classical modulus of continuity and second order modulus of continuity. We also investigate the rate of convergence of new operators for functions belonging to Lipschitz class and finally, we give an upper bound for the error of approximation via modulus of continuity of the derivative of approximating function.King Abdulaziz University, Jeddah, Saudi ArabiaThe authors gratefully acknowledge the financial support from King Abdulaziz University, Jeddah, Saudi Arabia