On the modified beta approximating operators of first kind - Vasile Miheşan (Journal of Numerical Analysis and Approximation Theory, 2004)
We define a general linear operator from which we obtain as special case the modified beta first kind operator\[(B_{p,q}f)(x)={B(p,q)}\int_0^1 t^{p-1}(1-t)^{q-1}f\left({B(p,q)}{B(p+a,q)}t^a x\right){\rm d}t.\]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.