We introduce a -generalization of Szász-Mirakjan operators and discuss their properties for fixed . We show that the -Szász-Mirakjan operators have good shape-preserving properties. For example, are variation-diminishing, and preserve monotonicity, convexity, and concave modulus of continuity. For fixed , we prove that the sequence converges to uniformly on for each , where is the limit -Bernstein operator. We obtain the estimates for the rate of convergence for by the modulus of continuity of , and the estimates are sharp in the sense of order for Lipschitz continuous functions.
Heping Wang. Fagui Pu. Kai Wang. "Shape-Preserving and Convergence Properties for the -Szász-Mirakjan Operators for Fixed ." Abstr. Appl. Anal. 2014 (SI10) 1 - 8, 2014. https://doi.org/10.1155/2014/563613