Close to convex harmonic mappings

In this thesis, new subclasses of close-to-convex harmonic functions are investigated. The study consists of five chapters. In the first and second chapters, the aim and scope of the thesis and the basic definitions and theorems that will be used in the study are given. In the third chapter, some studies related to the subject discussed are examined. In the fourth chapter, new subclasses of harmonic functions containing second and third order differential inequalities are introduced. Some properties of these classes, such as close to convexity, coefficient bounds, and growth estimates are obtained. In addition, convex combination and convolution properties of these classes are obtained. Finally, harmonic polynomials involving Gaussian hypergeometric function belonging to these classes are construted. In the fifth chapter, the results obtained in the study are evaluated.