BETTER APPROXIMATION AND THEORETICAL VALIDATION FOR INTEGRAL-TYPE OPERATORS

This study is on an innovative technique of integral-type operators that adopt the Baskakov basis function in recursion form and the Sz\'{a}sz basis function, accentuating how well they approximate integrable functions. The study addresses the challenge of achieving more accurate function approximation, and mainly contributes to improving the theoretical aspects of the proposed operators. We examine the convergence properties of the proposed operators by employing Peetre's $K$-functional, second-order modulus of smoothness, and modulus of continuity. Additionally, we derive the Voronovskaja-type asymptotic formula and establish approximation results in weighted spaces. Finally, we show that the proposed operators significantly enhance the approximation accuracy through various examples and graphs.