Global Minimization of Best Proximity Points for Some Nonlinear Mappings and Some Algorithms for Solving Unconstrained Convex Optimization Problems

Abstract

In this thesis, we study two major problems in mathematics namely fixed point problem and varionational inequality problem. For the former, we study a more general problem which is a best proximity point problem. We introduce new mappings which extend some well-known results in the literature. Also, for each newly established mapping, we provide an existence theorem for a best proximity point as well as some examples to ensure the existence of our mapping. An algorithm for finding a best proximity point under some suitable conditions is also given. As for the latter problem, we construct new algorithms for solving a more general problem as well as some numerical examples to observe the behavior of the newly constructed algorithms. So our results can be applied to a wider class of problems.