In 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.
Braha NL, Srivastava HM, Mohiuddine SA (2014) A Korovkin’s type approximation theorem for periodic functions via the statistical summability of the generalized de la Vallée Poussin mean. Appl Math Comput 228:162–169MathSciNetzbMATHGoogle Scholar
Burban I (1995) Two-parameter deformation of the oscillator algebra and \((p, q)\) analog of two dimensional conformal field theory. Nonlinear Math Phys 2(3–4):384–391MathSciNetCrossRefzbMATHGoogle Scholar
Burban IM, Klimyk AU (1994) \(P, Q\) differentiation, \(P, Q\) integration and \(P, Q\) hypergeometric functions related to quantum groups. Integral Transform Spec Funct 2(1):15–36MathSciNetCrossRefzbMATHGoogle Scholar
Jagannathan R, Rao KS (2005) Two-parameter quantum algebras, twin-basic numbers, and associated generalized hypergeometric series. In: Proceedings of the international conference on number theory and mathematical physics, pp 20–21Google Scholar