On Mellin-type Integral Operators preserving x a and x2a, a >0

In this paper we study a general class of Mellin-type integral operators that preserve the functions x a and x2a , with a >0. Weighted convergence with respect to certain weights is studied. Moreover quantitative estimate, using a suitable modulus of continuity, and an asymptotic formula are obtained. Finally the theory is applied to various specific examples.