Approximation with an arbitrary order by generalized Kantorovich-type and Durrmeyer-type operators on [0, +∞) - TRIFA, Sorin (Studia Universitatis Babeș-Bolyai Mathematica, 2017)
Given an arbitrary sequence λn > 0, n ∈ N, with the property that limn→∞ λn = 0 as fast we want, in this note we introduce modified/ gene- ralized Sza´sz-Kantorovich, Baskakov-Kantorovich, Sza´sz-Durrmeyer-Stancu and Baskakov-Sza´sz-Durrmeyer-Stancu operators in such a way that on each compact subinterval in [0, +∞) the order of uniform approximation is ω1(f ; √λn). These modified operators uniformly approximate a Lipschitz 1 function, on each com- pact subinterval of [0, ∞) with the arbitrary good order of approximation √λn. The results obtained are of a definitive character (that is are the best possible) and also have a strong unifying character, in the sense that for various choices of the nodes λn, one can recapture previous approximation results obtained for these operators by other authors. Mathematics Subject Classification (2010): 41A36, 41A25.