NONLINEAR APPROXIMATION BY q-FAVARD-SZÁSZ-MIRAKJAN OPERATORS OF MAX-PRODUCT KIND

Approximation by max-product type nonlinear operators

The purpose of this survey is to present some approximation and shape preserving properties of the so-called nonlinear (more exactly sublinear) and positive, max-product operators, constructed by starting from any discrete linear approximation operators, obtained in a series of recent papers jointly written with B. Bede and L. Coroianu. We will present the main results for the max-product opera...

Modified double Szász - Mirakjan operators preserving x

In this paper, we introduce a modification of the Szász-Mirakjan type operators of two variables which preserve f0 (x, y) = 1 and f3 (x, y) = x 2 + y. We prove that this type of operators enables a better error estimation on the interval [0,∞) × [0,∞) than the classical Szász-Mirakjan type operators of two variables. Moreover, we prove a Voronovskaya-type theorem and some differential propertie...

Approximation of fuzzy numbers by nonlinear Bernstein operators of max-product kind

In this paper firstly we extend from [0, 1] to an arbitrary compact interval [a, b], the definition of the nonlinear Bernstein operators of max-product kind, B n (f), n ∈ N, by proving that their order of uniform approximation to f is ω1(f, 1/ √ n) and that they preserve the quasi-concavity of f . Since B (M) n (f) generates in a simple way a fuzzy number of the same support [a, b] with f , it ...

Max-Product Shepard Approximation Operators

In crisp approximation theory the operations that are used are only the usual sum and product of reals. We propose the following problem: are sum and product the only operations that can be used in approximation theory? As an answer to this problem we propose max-product Shepard Approximation operators and we prove that these operators have very similar properties to those provided by the crisp...

Approximation by Lupas-Type Operators and Szász-Mirakyan-Type Operators