On Some Positive Linear Operators Preserving the B^{-1}-Convexity of Functions

Abstract

In the study, we first give an inequality that non-negative differentiable functions must satisfy to be B^{-1}-convex. Then, using the inequality, we show that the B^{-1}-convexity property of functions is preserved by Bernstein-Stancu operators, Sz'asz-Mirakjan operators and Baskakov operators. In addition, we compare the concepts B^{-1}-convexity and B-concavity of functions.

Keywords

• B−1 -convexity
• Bernstein-Stancu operators
• Sz´asz-Mirakjan operators
• Baskakov operators
• Shape preserving approximation.

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