Ibragimov–Gadjiev operators preserving exponential functions

Abstract

Abstract In this paper, a modification of general linear positive operators introduced by Ibragimov and Gadjiev in 1970 is constructed. It is shown that this modification preserves exponential mappings and also contains modified Bernstein-, Szász- and Baskakov-type operators as special cases. The convergence properties of corresponding operators on [ 0 , ∞ ) $[ 0,\infty ) $ and in exponentially weighted spaces are investigated. Finally, the quantitative Voronovskaja theorem in terms of modulus of continuity for functions having exponential growth is examined.

Keywords

• Ibragimov
• Gadjiev operators
• Modified Bernstein-type operators
• Szász
• Mirakjan operators
• Modulus of continuity