Some Studies in Complex function Theory The present thesis is based on the study of recent works in complex function theory by eminent scholars like Ahuja, Andrews, Aouf, Ganesan, Jahangiri, Janowski, Khalida Inayat Noor, Kulkarni, Milin, Moulis, Murugusundaramoorthy, Nanjunda Rao, Paatero, Parvatham, Ruscheweyh, Silverman, Silvia, Shivaprasad, Owa, and others. We have made an extensive study of operators like Ruscheweyh operator D_f(z), S?al?agean operator Dnf(z), Al-Oboudi generalized S?al?agean operator Dn_ f(z) and the operator _f(z) defined by using the fractional derivative D_ zf(z). In recent years, there have been many papers in which several subclasses are defined using these operators. These operators help to unify many well known classes of analytic functions and to obtain generalized results. We study several properties of functions of these classes thereby giving a unified approach to proving and at the same time generalizing many results that have been obtained earlier in literature. An attempt has been made to have a detailed study by employing different techniques.