On approximation properties by exponential type of Bernstein-Stancu Operators

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In the paper, we introduced a generalization of Bernstein-Stancu-Kantorovich operators that reproduces exponential functions. For appropriate function spaces, both the uniform and L^p convergence have been established. We proved that the new operators satisfy the Korovkin tests with the exponential functions and calculated the operators’ analytical expressions evaluated on various powers of e ^μxwhich is necessary to get the uniform convergence conclusion using the well-known Korovkin Theorem. Consequently, the convergence theorem for the new operators, which transfer the weighted space L_μ^p ([0,1]) to itself, has been established. Additionally, using the usual modulus of continuity of the estimated function in the continuous case, we provide quantitative estimates for the approximation error.