Functional analysis is the study of certain topological algebraic structures and of the methods by which knowledge of these structures can be applied to analytic problems. It is provided with many fundamental notions relevant for the description, analysis, numerical approximation and computer simulation process. Fixed point theorem plays a prominent role in pure and applied mathematics. The achievement in the field of functional analysis in last few decades is mainly the development of new imaginative way to use the fundamental tools of the functional analysis. The problems associated in the present research work are related to the study of fixed point theorems in cone metric spaces, coincidence point, common fixed point, common fixed point theorems for multivalued maps, T-contractive mappings along with the application c-distance of fixed point theorem in cone metric space.