This thesis consists of five chapters. The first chapter which serves as an introductions to the remaining part of the thesis, contains the fundamental concepts and results relevant to the subject matter of investigation taken up in this thesis. The idea is to make the thesis self contained as far as possible reference are given to source from which they are taken. The second and third fourth and fifth chapters embody the original reults of the author's investigation. The second chapter contains the result on multivalent functions with negative coefficients. In the thord chapter Bazilevic class of function are studied. Certain properties of prestarlike functions are studied in fourth chapter. The last chapter contains results on meromorphic functions.
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