The College of Education for Pure Sciences, Department of Mathematics, organized a scientific lecture on the theory of geometric functions generated by quantitative differential and integral calculus and related to some special functions. The lecture, presented by the student (Sareem Hazem Hadi), included the introduction of new types of complex analytical classes in the field of the open unit disc of the equivalent type, inverse equivalence and multivalent. The doctor presented his study on estimating the value of parameters and the upper and lower limits of analytical functions. In addition, a study was presented on finding the values ​​of inequalities for the Hankel and Toeplitz criterions. In addition to the study of harmonic analytical functions of the equivalent and multivalent types. Some statistical applications were also discussed regarding the study.