Usta, Fuat2023-07-262023-07-2620220139-99181337-2211https://doi.org/10.1515/ms-2022-0085https://hdl.handle.net/20.500.12684/12308Balazs operators are an influential tool that can be used to approximate a function on the unbounded interval [0, infinity). In this study, a new construction of Balazs operators which depending upon on a function rho(x) has been introduced. The function rho(x) plays a significant role in this construction due to the fact that the new operator preserves definitely two test functions from the set of {1, rho(x), rho(2)(x)}. In this direction, the approximation properties of this newly defined operators are established, such as degree of approximation and Voronovskaya type theorems. Finally, we presented a set of computational examples in order to validate the new construction of operator is an approximation procedure.en10.1515/ms-2022-0085info:eu-repo/semantics/closedAccessBalazs Type Operators; Voronovskaya Type Theorem; Rate Of Convergence; Weighted Approximation; Numerical ExperimentsBezier VariantArticle725124512582-s2.0-85140489542WOS:000868352700009Q2Q1