Approximation by a family of summation-integral type operators preserving linear functions

This article investigates the approximation properties of a general family positive linear operators defined on unbounded interval [0,?). We prove uniform convergence theorem and Voronovskayatype for functions with polynomial growth. More precisely, we study weighted i.e basic theorems, quantitative Voronovskaya-asymptotic theorems Gr?ss in spaces. Finally, obtain rate these via suitable modulus continuity.