×

\(A\)-statistical convergence for a class of positive linear operators. (English) Zbl 1174.41312

Summary: We introduce a sequence of positive linear operators defined on the space \(C[0,a]\) \((0<a<1)\), and provide an approximation theorem for these operators via the concept of \(A\)-statistical convergence. We also compute the rates of convergence of these approximation operators by means of the first and second order modulus of continuity and the elements of the Lipschitz class. Furthermore, by defining the generalization of \(r\)-th order of these operators, we show that the similar approximation properties are preserved on \(C[0,a]\).

MSC:

41A10 Approximation by polynomials
41A25 Rate of convergence, degree of approximation
41A36 Approximation by positive operators
40A25 Approximation to limiting values (summation of series, etc.)
PDFBibTeX XMLCite