Contributions to the theory of special univalent functions

In this thesis, we mainly focus on coefficient problem for some subclasses of bi-univalent functions and geometric properties of Wright functions. k-bi-starlike functions belonging to the class S_(σ,k)^⋆ defined by making use of the Sӑlӑgean derivative operator which are subclasses of bi-univalent functions are introduced and its some properties are studied. Moreover, upper bound estimate for the second Hankel determinant for functions defined by convolution belonging to the class N_σ^(μ,δ) (λ,t) by using Chebyshev polynomials are found. Finally, we find the radii of starlikeness and convexity of the normalized Wright functions. In addition, by using the Euler-Rayleigh inequalities we obtain some tight lower and upper bounds for the radii of starlikeness and convexity of order zero for the normalized Wright functions.