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In the present paper, convergence in modular spaces is investigated for a class of nonlinear discrete operators, namely the nonlinear multivariate sampling Kantorovich operators. The convergence results in the Musielak-Orlicz spaces, in the weighted Orlicz spaces, and in the Orlicz spaces follow as particular cases. Even more, spaces of functions equipped by modulars without an integral representation are presented and discussed.

Convergence Results for Nonlinear Sampling Kantorovich Operators in Modular Spaces