Shape Preserving Properties for q-Bernstein-Stancu Operators

الملخص EN

We investigate shape preserving for q-Bernstein-Stancu polynomialsBnq,α(f;x) introduced by Nowak in 2009.

When α=0, Bnq,α(f;x) reduces to the well-knownq-Bernstein polynomials introduced by Phillips in 1997; when q=1, Bnq,α(f;x) reduces toBernstein-Stancu polynomials introduced by Stancu in 1968; when q=1, α=0, we obtain classical Bernstein polynomials.

We prove that basic Bnq,α(f;x) basis is a normalizedtotally positive basis on [0,1] and q-Bernstein-Stancu operators are variation-diminishing, monotonicity preserving and convexity preserving on [0,1].