Approximation of Generalized Szász-Mirakjan Operators Depending on certain Parameters

Abstract

Motivated by certain generalizations, in this paper we consider a new analogue of generalized Sz´asz-Mirakjan operators whose construction depends on τ, with extra parameters μ and λ. Depending on the selection of μ and λ, these operators are more flexible than the generalized Sz´asz-Mirakjan operators. We investigate approximation properties. Also, we study local and global approximation, Voronovskaya type theorem. Finally, quantitative estimates for the local approximation are discussed.

Key words and phrases. Positive Operators, Voronovskaya type theorem, Weighted modulus of continuity, Local approximation.

2010 Mathematics Subject Classification. 41A10, 41A25, 41A36