On approximation of functions by polynomials with weight (Q1207385)

The author develops an inequality similar to Jackson's inequality for the approximation \[ E_ n(P,\alpha,\beta,f)=\inf_{P_ n\in\Pi_ n}\| f-P_ n\|_{P,\alpha,\beta},n\in N, \] where \(\Pi_ n\) denotes that set of all algebraic polynomials of degree at most \(n\), and \(N\) is the set of nonnegative integers. The author also improves a result on direct and converse theorem for the above best approximation.