Some geometric properties of Miller-Ross and Rabotnov functions

In this thesis, firstly, sufficient conditions were obtained for the Dini function, which is a special combination of Bessel functions, to be included in the classes of k-starlike and k-uniformly convex functions; then, sufficient conditions are given for the generalized Dini function to be included in some subclasses of starlike and convex functions. Moreover, the geometric properties of the Miller-Ross function given by K.S. Miller and B.Ross in 1993 and the Rabotnov function, which is a fractional exponential function given by Yu.N.Rabotnov in 1948, are investigated and sufficient conditions have been obtained for these functions to be univalent, convex, starlike and close-to-convex in the unit disk U .