The College of Education for Pure Sciences, Department of Mathematics, examined a master's thesis on "Approximation Using Specific Paskakoff Operators." The thesis, submitted by researcher Hanin Falah Abdul Hassan, presents a new family of positive linear operators within the framework of approximation theory. This is achieved by introducing flexible generalizations of certain Paskakoff sequences that rely on two non-negative parameters: a non-negative integer and a real number. The proposed sequences not only reduce the values ​​of the error function but also offer flexibility in handling different types of test functions that contain parameters, highlighting the potential of this proposed sequence as a more flexible and effective tool for approximation.

Three main generalizations were studied: the Paskakoff sequence of type , the half-Paskakoff sequence of type , and the Paskakoff-Kantorovitch sequence of type . For each of these sequences, the 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 and . For each case, the average of the absolute errors was calculated and compared with different choices of the two parameters. The numerical results show that the accuracy of the approximation can be improved by appropriately choosing the two parameters, and this varies depending on the function chosen.

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