The College of Science, Department of Mathematics, discussed a doctoral dissertation entitled " Better Approximation by New Bivariate GBS – Sequences of Linear Positive Operators" by postgraduate student Ahmed Fadhil Jabbar. The thesis aims to present three innovative and detailed modifications of classical Baskakov operator sequences and conduct a comprehensive study of the ordinary approximation of unbounded functions, which are functions that do not adhere to specific constraints on their values. It also includes a deeper understanding of how these operators approximate the original functions. In addition, the dissertation addresses a discussion and in-depth analysis of various approximation theories related to these operators, focusing on both positive and non-positive operators. Furthermore, the study examines Voronovskaja's approximate formulas for these operators, which provide accurate information about the convergence rate between the operators and the original functions as the variable n approaches infinity, and determines the frequency relationship of the moment of order m. It also investigates the convergence rates using powerful analytical tools such as the continuity coefficient and Lipschitz space. The study concludes that the error in the approximation is inversely proportional to a certain power of n, where n represents the number of terms in the sequence.
