Bivariate Mellin convolution operators: Quantitative approximation theorems

In this paper we study some qualitative and quantitative versions of the Voronovskaja approximation formulae for a class of bivariate Mellin convolution operators of type ( T w f ) ( x , y ) = ∫ R + 2 K w ( t x − 1 , v y − 1 ) f ( t , v ) d t d v t v . Moreover we apply the general theory to some particular cases leading to various asymptotic formulae and involving various differential operators.