Weighted approximation of functions by Favard operators of max-product type

New approximation properties of the Bernstein max-min operators and Bernstein max-product operators

“…As an alternative to the well-known linear approximation operators, recently, various types of nonlinear approximation operators have been introduced. First, we mention the so called max-product type operators, a class of subadditive and positively homogeneous operators, used as alternatives for the linear counterparts in many areas such as, approximation operators (see, e. g., [2], [3], [20]), interpolation operators (see, e. g., [5], [9]), sampling operators (see, e. g., [6], [8]), neural network operators (see, e. g., [1], [13], [14]) and others (see, e. g. [18], [17], [19], [21]). A detailed account on the theory of max-product type operators can be found in the monograph [4].…”

Inverse Result of Approximation for the Max-Product Neural Network Operators of the Kantorovich Type and Their Saturation Order

“…In general, the max-product version of a sequence/net of linear operators is a family of nonlinear (more precisely sub-linear) operators with better approximation properties of their original version: in many cases, the order of convergence is faster than their linear counterparts [4][5][6]. Further, the above operators can also be useful, for instance, in the applications of probability and fuzzy theory involving both real and interval/set valued functions (see, e.g., [7,8]).…”