RATE OF CONVERGENCE OF KANTOROVICH OPERATORS IN MORREY SPACES
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 c...
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| Format: | Theses |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/68542 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | 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 |
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