Modified double Szasz-Mirakjan operators preserving x2 + y2

In this paper, we introduce a modification of the Szasz-Mirakjan type operators of two variables which preserve f(0)(x, y) = 1 and f(3)(x, y) = x(2) + y(2). We prove that this type of operators enables a better error estimation on the interval [0, infinity) x [0, infinity) than the classical Szasz-Mirakjan type operators of two variables. Moreover, we prove a Voronovskaya-type theorem and some differential properties for derivatives of the semodified operators. Finally, we also study statistical convergence of the sequence of modified Szasz-Mirakjan type operators.