Functional inequalities for some special functions

In this thesis, studies have been made on the functional inequalities of several some special functions, including the Ramanujan type entire function, the modified q- Tricomi function, the q-Bessel function and the q- Struve Bessel function. The main objective of the study focuses on two fundamental problems. First, various new Turán type inequalities for the Ramanujan type entire function and the modified q- Tricomi function are obtained. In addition, several Turán type inequalities concerning the remainder terms in the series expansions of these functions are also established. Second, the monotonicity properties of the Ramanujan type entire function, as well as those of the Bessel and q- Struve Bessel functions, are investigated by employing the subordinating factor sequence method.