On the modified beta approximating operators of first kind - Miheşan, Vasile (Rev. Anal. Numér. Théor. Approx., 2004)
We define a general linear operator from which we obtain as special case the modified beta first kind operator\[(B_p,qf)(x)=B(p,q)_0^1 t^p-1(1-t)^q-1f(B(p,q)B(p+a,q)t^a x)dt.\]We consider here only the cases \(a=1\) and \(a=-1\).We obtain several positive linear operators as particular cases of this modified beta first kind operator.