Geometric properties of new subclass of univalent and bi-univalent functions associated with subordination and generalised differential operator

Hence, motivated by the generalised differential operator in the second objective, this study proposed a new generalised differential operator by utilising the binomial series. This new operator is applied in obtaining the inclusion properties for the class of analytic univalent functions. Then, the results on covering theorem, distortion theorem, rotation theorem, growth theorem, and the radius of convexity for functions of the class of bi-univalent functions were derived by utilising the new differential operator. The final chapter of this thesis discussed on the suggestion problems for future research. In conclusion, this thesis introduces new subclasses of univalent and bi-univalent functions and extends several classical results in geometric function theory. The findings contribute significantly to the understanding of these classes, offering new techniques and insights for future research.