On the β-modification of the Mellin-Gauss-Weierstrass kernel and its related information potential

In the current study, we investigate the behaviour of -modification of the Mellin-Gauss-Weierstrass (MGW) type operators with respect to pointwise and uniform convergence.Moreover, we give a Voronovskaya approximation formula for the MGW type operators using the new kernel.This formula contains Mellin derivatives and a different notion of moment which was called the logarithmic moment.In the last part, we analyze the related information potential, the variance V [logp( , )] and expected value EV [logp( , )] using the modified MGW kernel p(, ) .