Nonlinear sampling Durrmeyer operators: approximation results in function spaces

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 α log β L − spaces) and exponential type spaces. Finally, various applications and examples, including graphical representations, are provided.