Abstract
Abstract Balázs operators are an influential tool that can be used to approximate a function on the unbounded interval [0, ∞). In this study, a new construction of Balázs operators which depending upon on a function ρ(x) has been introduced. The function ρ(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, ρ(x), ρ 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.
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