RATE OF CONVERGENCE OF KANTOROVICH OPERATORS IN MORREY SPACES

• Main Author: Gunadi, Reinhart
• Format: Theses
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/68542
• Institution: Institut Teknologi Bandung

The Kantorovich operators Kn, n 2 N is a modification of Bernstein polynomials to approximate integrable functions on [0, 1], including functions that are not continuous. The convergence of Kantorovich operators has been studied in the Lebesgue spaces Lp([0, 1]). In this thesis, we consider the convergence of Kantorovich operators in the Morrey spaces Mpq ([0, 1]). Although it has yet to be established for arbitrary functions inMpq ([0, 1]), this kind of convergence is valid for all functions in C([0, 1])Mpq , which is the subset of functions inMpq ([0, 1]) that can be approximated by continuous functions on [0, 1]. Estimates for the rate of convergence of Kantorovich operators in Mpq ([0, 1]) is obtained by considering certain classes of functions. Here we consider functions in C0,?([0, 1]) and W1Mpq ([0, 1]), which is, respectively, the set of H¨older continuous functions with exponent ? and the set of absolutely continuous functions whose first derivative is inMpq ([0, 1]). The Kantorovich operators for functions in C0,?([0, 1]) converges in Mpq ([0, 1]) with the order of n