National Natural Science Foundation of China [61170324]; Class A Science and Technology Project of Education Department of Fujian Province of China [JA12324]; Natural Science Foundation of Fujian Province of China [2010J01012]We introduce summation-integral-type q-Szasz-Mirakjan operators and study approximation properties of these operators. We establish local approximation theorem. We give weighted approximation theorem. Also we estimate the rate of convergence of these operators for functions of polynomial growth on the interval [0,infinity]
