The College of Education for Pure Sciences in the Department of Mathematics researched a master's thesis on improving the classical Baskakov and Baskakov-Kantorovich sequences by presenting modifications that contribute to reducing the arithmetic operations and improving the accuracy of approximation. The thesis presented by the researcher (Ali Asaad Jadou) included improving these sequences through two main modifications: First, by taking half of the terms of the classical sequence, which helped reduce the required arithmetic operations. Second, by generalizing classical sequences by introducing the parameter r (a non-negative integer), which led to improving the approximation order and reducing the error function. The convergence of these sequences was studied using Korovkin's theorem, and the equivalent formula for Fronvisk's theorem was derived, with the approximation error calculated using the continuity coefficient. The theoretical aspects were supported by numerical examples comparing the results calculated using the modified and generalized sequences with the numerical results calculated using the classical sequences. The graphs and tables of numerical values showed the efficiency of the generalized sequences in terms of approximation accuracy and reducing the error function, confirming the effectiveness of these modifications in improving approximation techniques in various mathematical applications
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