The concept of mixed-norm spaces has emerged as a significant interest in fields such as harmonic analysis. In addition, the problem of function approximation through sampling series has been particularly noteworthy in approximation theory. In this paper, we study the approximation problem in diverse mixed-norm function spaces. We utilize the family of Kantorovich-type sampling operators as approximator for the functions in mixed-norm Lebesgue space \(L^{\overrightarrow{P}}(\mathbb {R}^n),\) with \( \overrightarrow{P}=(p_1,p_2,\dots ,p_n),\) and mixed-norm Orlicz space \(L^{\overrightarrow{\Phi }}(\mathbb {R}^n),\) with \(\overrightarrow{\Phi }=\left( \phi _{1},\phi _{2},\dots , \phi _{n} \right) ,\) where each \(\phi _{i}\) is an Orlicz function (defined in Section 2). The Orlicz spaces are a generalized family that encompasses many significant function spaces. We establish the boundedness of the family of generalized and Kantorovich-type sampling operators within the framework of these mixed-norm spaces. Further, we study the approximation properties of Kantorovich-type sampling operators in both mixed-norm Lebesgue and Orlicz spaces. Lastly, we provide several examples of appropriate kernels that demonstrate the applicability of the proposed theory.
