Preservation of Lipschitz constants by Bernstein type operators

Abstract

We obtain preservation inequalities for Lipschitz constants of higher order in simultaneous approximation processes by Bernstein type operators. From such inequalities we derive the preservation of the corresponding Lipschitz spaces.

Generalized Szász-Mirakian Type Operators

“…Hermann considered this operator on a much wider class, growing faster than exponentially. In 2005, Schurer [6,7] type generalization was given by Moreno [4] for this operator 1.1.…”

Convergence of Special Sequences of Semi-Exponential Operators

“…(B) Exponential operators. Some important operators, called exponential operators, were intensively investigated in several papers (see, e.g., [7][8][9][10][11][12][13][14]).…”