On the modified beta approximating operators of second kind

Abstract

We shall define a general linear operator from which we obtain as particular case the modified beta second kind operator$$(T_{p,q}f)(x)=\frac{1}{B(p,q)}{\int }_0^{\mathrm{\infty }}\frac{u^{p-1}}{(1+u{)}^{p+q}}f\left(\frac{B(p,q)}{B(p+a,q-a)}{u}^{a}x\right)\mathrm{d}u.$$ We consider here only the case $a=1$. We obtain several positive linear operators as a particular case of this modified beta second kind operator.