L p approximation by general Bernstein-Durrmeyer operator defined on simplex
Copyright policy )L p approximation by general Bernstein-Durrmeyer operator defined on simplex
Let \(Q \) be the simplex in \(R^d\) defined by \(x_i\geq 0\) and \(\sum x_i \leq 1\), and let \(L^p(Q)\) be the Lebesgue spaces for \(1\leq p <\infty\) and \(L^\infty =C(Q)\) the space of continuous functions with maximum norm. The author defines a class of general Bernstein-Durrmeyer operators \(L_n\) which assign to a function \(f\in L^p\) a linear combination of Bernstein polynomials of total degree \(n-s\). The parameter \(s\) is an integer in the range \(0 \leq s
- Xi’an Jiaotong-Liverpool University China (People's Republic of)
- Florida State University College of Arts and Sciences United States
Inverse theorems in approximation theory, Approximation by positive operators, Multidimensional problems, Bernstein-Durrmeyer operators, Rate of convergence, degree of approximation, degree of approximation, direct theorem, inverse theorem, moduli of smoothness, multidimensional \(L^p\) approximation
Inverse theorems in approximation theory, Approximation by positive operators, Multidimensional problems, Bernstein-Durrmeyer operators, Rate of convergence, degree of approximation, degree of approximation, direct theorem, inverse theorem, moduli of smoothness, multidimensional \(L^p\) approximation
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