The College of Education for Pure Sciences, Department of Mathematics, organized a scientific lecture on approximation using specific Paskakov operators. The lecture, presented by researcher Hanin Falah Abdulhassan, introduced a new family of positive linear operators within approximation theory. This was achieved by presenting flexible generalizations of certain Paskakov sequences that depend on two non-negative parameters: a non-negative integer r and a real number α∈[0,1]. The proposed sequences not only minimize the error function but also offer flexibility in handling different types of test functions with parameters, highlighting their potential as a more flexible and effective approximation tool. For each of these sequences, convergence was proven using Korfkin's theorem. Furthermore, error estimates were derived in terms of the continuity coefficient, and the equivalent formula for Vronevsky's theorem was obtained. Finally, a numerical example was presented in which a test function was approximated for different values of r and α. For each case, the average of the absolute errors was calculated and compared with different parameter choices. The numerical results show that the approximation accuracy can be improved by appropriately choosing the parameters r and α, and this varies depending on the chosen function
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