Approximation Results for Urysohn-Type Nonlinear Bernstein Operators
In the present work, our aim of this study is generalization and extension of the theory of interpolation of functions to functionals or operators by means of Urysohn-type nonlinear operators. In accordance with this purpose, we introduce and study a new type of Urysohn-type nonlinear operators. In particular, we investigate the convergence problem for nonlinear operators that approximate the Urysohn-type operator. The starting point of this study is motivated by the important applications that approximation properties of certain families of nonlinear operators have in signal–image reconstruction and in other related fields. We construct our nonlinear operators by using a nonlinear forms of the kernels together with the Urysohn-type operator values instead of the sampling values of the function. As far as we know, this will be first use of such kind of operators in the theory of interpolation and approximation. Hence, the present study is a generalization and extension of some previous results.
KeywordsUrysohn integral operators Nonlinear Bernstein operators Urysohn-type nonlinear Bernstein operators Approximation.
AMS Subject Classification41A25 41A35 47G10 47H30.
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