{Reference Type}: Journal Article
{Title}: Shape-preserving properties of a new family of generalized Bernstein operators.
{Author}: Cai QB;Xu XW;
{Journal}: J Inequal Appl
{Volume}: 2018
{Issue}: 1
{Year}: 2018
暂无{DOI}: 10.1186/s13660-018-1821-9
{Abstract}: In this paper, we introduce a new family of generalized Bernstein operators based on q integers, called ( α , q ) -Bernstein operators, denoted by T n , q , α  ( f ) . We investigate a Kovovkin-type approximation theorem, and obtain the rate of convergence of T n , q , α  ( f ) to any continuous functions f. The main results are the identification of several shape-preserving properties of these operators, including their monotonicity- and convexity-preserving properties with respect to f ( x ) . We also obtain the monotonicity with n and q of T n , q , α  ( f ) .