Recent zbMATH articles in MSC 41A35 https://www.zbmath.org/atom/cc/41A35 2022-05-16T20:40:13.078697Z Werkzeug Connections between the approximation orders of positive linear operators and their max-product counterparts https://www.zbmath.org/1483.41007 2022-05-16T20:40:13.078697Z "Coroianu, Lucian" https://www.zbmath.org/authors/?q=ai:coroianu.lucian-c "Costarelli, Danilo" https://www.zbmath.org/authors/?q=ai:costarelli.danilo "Gal, Sorin G." https://www.zbmath.org/authors/?q=ai:gal.sorin-gheorghe "Vinti, Gianluca" https://www.zbmath.org/authors/?q=ai:vinti.gianluca Authors establish some direct connections between arbitrary positive linear operators and their corresponding nonlinear (more exactly sublinear) max-product versions, with respect to uniform and \(L^p\) convergence. There are numerous concrete examples of approximation operators, such as Bernstein-type operators, neural network operators, sampling operators and others, where the linear and the max-product versions converge both uniformly. Here, from the quantitative uniform approximation result for an arbitrary sequence of positive linear operators, a simple general method, a quantitative uniform approximation result for its max-product counterpart are deduced. Also convergence with respect to the \(L^p\)-norm involving the well-known K-functionals, when the supremum of the kernel is bounded from below is established. Reviewer: Vijay Gupta (New Delhi) Reconstruction of two approximation processes in order to reproduce \(e^{ax}\) and \(e^{2ax}\), \(a>0\) https://www.zbmath.org/1483.41009 2022-05-16T20:40:13.078697Z "Yılmaz, Başar" https://www.zbmath.org/authors/?q=ai:yilmaz.basar "Uysal, Gümrah" https://www.zbmath.org/authors/?q=ai:uysal.gumrah "Aral, Ali" https://www.zbmath.org/authors/?q=ai:aral.ali The authors proposed two modifications for Gauss-Weierstrass operators and moment-type operators which fix \(e^{ax}\) and \(e^{2ax}\), \(a>0\). They studied weighted approximation and proved Voronovskaya-type theorems in exponentially weighted spaces. Using the modulus of continuity in exponentially weighted spaces, they obtained some global smoothness preservation properties, and they gave a comparison result for Gauss-Weierstrass operators. Finally, they provided some graphical representations. Reviewer: Naokant Deo (Delhi)