In the present paper, we introduce a generalized Sz\'{a}sz type operators based on where is a continuously differentiable function on and . This function not only characterizes the operators but also characterizes the Korovkin set in a weighted function space. First, we establish approximation in a Lipschitz type space and weighted approximation theorems for these operators. Then we obtain a Voronovskaja type result and the rate of convergence in terms of the weighted modulus of continuity.