Approximation by max-product sampling Kantorovich operators with generalized kernels. (English) Zbl 1464.41004
Authors’ abstract: In a recent paper, for max-product sampling operators based on general kernels with bounded generalized absolute moments, we have obtained several pointwise and uniform convergence properties on bounded intervals or on the whole real axis, including a Jackson-type estimate in terms of the first uniform modulus of continuity. In this paper, first, we prove that for the Kantorovich variants of these max-product sampling operators, under the same assumptions on the kernels, these convergence properties remain valid. Here, we also establish the \(L_p\) convergence, and quantitative estimates with respect to the \(L_p\) norm, \(K\)-functionals and \(L_p\)-modulus of continuity as well. The results are tested on several examples of kernels and possible extensions to higher dimensions are suggested.
Reviewer: Włodzimierz Łenski (Poznań)
MSC:
| 41A25 | Rate of convergence, degree of approximation |
| 41A05 | Interpolation in approximation theory |
| 41A30 | Approximation by other special function classes |
| 47A58 | Linear operator approximation theory |
Keywords:
max-product sampling Kantorovich operators; generalized kernels; \(L_p\)-norm; \(1\leq p<\infty,K\)-functional; modulus of continuityReferences:
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