Abstract
The goal of this study is generalization and extension of the theory of interpolation of functions to functionals and operators. We investigate the convergence problem for linear positive operators that approximate the Urysohn type operator in some functional spaces. One of the main difference between the present work and convergence to a function lies in the use of the Urysohn type operator values instead of the sampling values of a function. From the definitions of the Urysohn type operators, Heaviside and Dirac Delta function, the current study can be also consider as convergence of a kind of nonlinear form of the classical linear positive operators to a function.
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Dedicated to my late father Cemal Karsli.
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Karsli, H. Approximation by Urysohn Type Meyer-König and Zeller Operators to Urysohn Integral Operators. Results Math 72, 1571–1583 (2017). https://doi.org/10.1007/s00025-017-0729-x
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DOI: https://doi.org/10.1007/s00025-017-0729-x