Integral inequalities on time scales for different kinds of convex functions

In this thesis, firstly convective function concept and types of convexity closely related to the theory of inequality are introduced. Convex function definition and averages have some features by way of relation. Then the time scale and the integrals are mentioned and then the definitions of differentiation and integration in the time scale are given. The basic concepts for the integrals in the time scale are reminded again. Some inequalities are presented in the literature, proved with the help of scalar integrals. In the research findings, m-convexity, convexity and quasi convexity are defined in time scale. New integral inequalities are obtained by applying m-convexity, convexity and quasi convexity definitions to Simpson-type integral inequality and m-convexity and quasi convexity definitions to Ostrowski-type integral inequality in time scales according to these definitions. In addition, results were obtained that included some special cases for the inequalities obtained and examples supporting these results were included.