Global Minimization of Best Proximity Points for Some Nonlinear Mappings and Some Algorithms for Solving Unconstrained Convex Optimization Problems - Panitarn Sarnmeta (เชียงใหม่ : บัณฑิตวิทยาลัย มหาวิทยาลัยเชียงใหม่, 2020)
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.