Volume 36 • Number 3 • 2013   • Statistical Approximation Properties of Modified $q$-Stancu-Beta Operators M. Mursaleen and Asif Khan Abstract. In this paper we define the modified $q$-Stancu-Beta operators and study the weighted statistical approximation by these operators with the help of the Korovkin type approximation theorem. We also establish the rates of statistical convergence by means of the modulus of continuity and the Lipschitz type maximal function. Our results show that rates of convergence of our operators are at least as fast as classical Stancu-Beta operators. 2010 Mathematics Subject Classification: Primary: 41A10, 41A25, 41A36; Secondary: 40A30 Full text: PDF