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Nonlinear sampling Durrmeyer operators: approximation results in function spaces
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DOI：10.1515/ans-2023-0210.png)
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Abstract
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In this paper we introduce and study the nonlinear version of sampling Durrmeyer operators. For what concerns the space of continuous functions, a pointwise and uniform convergence theorem have been established. Additionally, approximation results for nonlinear sampling Durrmeyer operators in the general setting of Orlicz spaces are also provided. In particular, a general modular convergence theorem has been obtained via a density approach. As a corollary, it follows that this theory applies to particular cases of Orlicz spaces, such as to L p - spaces, interpolation spaces (L alpha log beta L - spaces) and exponential type spaces. Finally, various applications and examples, including graphical representations, are provided.
Keywords:
sampling Durrmeyer type operators
Orlicz spaces
modular convergence
uniform convergence
generalized sampling operators
sampling Kantorovich operators
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