Better error estimation for Szász-Mirakjan-Beta operators - Duman, Oktay; Özarslan, Mehmet Ali; Aktu?lu, Hüseyin (My University, 2008)
In this paper, we present a modification of a sequence of mixed summation-integral type operators having Szász and Beta basis functions in summation and integration, the so-called Szász-Mirakjan-Beta operators. Then we show that our modified operators have a better error estimation on the interval [0, 2]. Furthermore, we give an r-th order generalization of the modified Szász-Mirakjan-Beta operators and investigate their approximation properties.
Keywords: Lipschitz class functionals; Modulus of continuity; Positive linear operators; Szász-Mirakjan-Beta operators; The Korovkin-type approximation theorem