| Abstract: |
| Among sampling type operators, the Generalized Durrmeyer-Sampling type series represents a generalization of both the Generalized and Kantorovich Sampling operators. The talk is focused on some recent approximation results for the Nonlinear version of Durrmeyer-Sampling type operators. \
For what concerns the space of continuous functions, a pointwise and uniform convergence theorem is provided. Moreover, approximation results for the nonlinear sampling Durrmeyer operators in the general setting of Orlicz spaces are also discussed. This results also ensures convergence in notable specific cases, such as in $L^p$-spaces, Zygmund spaces, and exponential spaces. Moreover, by considering the case of functions that are not necessarily continuous, these findings prove especially valuable in practical applications, where most real-world signals, such as digital images, are not mathematically represented by continuous functions. |
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