A study for Bernstein-Stancu operators keeping exponential functions

This thesis consists of eight chapters. The first chapter is devoted to the introduction. In the second part, some definitions and theorems that will be used in the thesis, basic concepts are given. In the third part, a general literature review is given to linear positive operators and their properties in chronological order. Approximation properties of the modified Bernstein-Stancu operator are given. In the sixth section, we present the point convergence of the modified Bernstein-Stancu operator and the Vronoskaya type theorem in quantitative mean that will allow both the targeted degree of convergence and the upper bound for the approximation error. Numerical examples are given. The eighth chapter is reserved for conclusions and suggestions. Keywords: Bernstein operator, Bernstein-Stancu operator, Positive linear operator, Bernstein-Stancu operator conserving exponential functions, Vronoskaya type theorems