Some Best Proximity Point Results for Multivalued Mappings

Fixed point theory is an exciting branch of mathematics. It is a mixture of analysis, topology and geometry. Fixed point techniques have been applied in fields such as biology, chemistry, economics, engineering and physics. It has very fruitful applications in control theory, game theory, category theory, functional equations, integral equations, mathematical physics, mathematical chemistry, functional analysis and many other areas. Thus, the study of the fixed point theory has been researched extensively in different metric spaces. On the other hand, by introducing the concept of the best proximity point, taking into account non-essential mappings, the fixed point results are expanded in a different sense. In this thesis, we obtain some best proximity point results for multivalued mappings via partial Hausdorff metric on partial metric spaces. Also, we obtain some new best proximity point results for cyclic multivalued mappings on partial metric spaces by considering Feng-Liüs technique.