Approximation properties of a new family of Gamma operators and their applications

Abstract

Abstract The present paper introduces a new modification of Gamma operators that protects polynomials in the sense of the Bohman–Korovkin theorem. In order to examine their approximation behaviours, the approximation properties of the newly introduced operators such as Voronovskaya-type theorems, rate of convergence, weighted approximation, and pointwise estimates are presented. Finally, we present some numerical examples to verify that the newly constructed operators are an approximation procedure.

Keywords

• Gamma operators
• Modulus of continuity
• Voronovskaya theorem
• Korovkin-type theorem
• Shape-preserving approximation