Shape-Preserving and Convergence Properties for the -Szász-Mirakjan Operators for Fixed

Heping Wang, Fagui Pu and Kai Wang

Abstract and Applied Analysis, 2014, vol. 2014, 1-8

Abstract:

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.

Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:563613

DOI: 10.1155/2014/563613

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