Quantitative estimates for perturbed sampling Kantorovich operators in Orlicz spaces - Costarelli Danilo; De Angelis Eleonora; Vinti Gianluca (Demonstratio Mathematica)
In the present work, we establish a quantitative estimate for the perturbed sampling Kantorovich operators in Orlicz spaces, in terms of the modulus of smoothness, defined by means of its modular functional. From the obtained result, we also deduce the qualitative order of approximation, by considering functions in suitable Lipschitz classes. This allows us to apply the above results in certain Orlicz spaces of particular interest, such as the interpolation spaces, the exponential spaces and the LpL^{p}-spaces, 1≤p<+∞1\le p\lt +∞ . In particular, in the latter case, we also provide an estimate established using a direct proof based on certain properties of the LpL^{p}-modulus of smoothness, which are not valid in the general case of Orlicz spaces. The possibility of using a direct approach allows us to improve the estimate that can be deduced as a consequence of the one achieved in Orlicz spaces. In the final part of the article, we furnish some estimates and the corresponding qualitative order of approximation in the space of uniformly continuous and bounded functions.