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

• Main Author: Panitarn Sarnmeta
• Other Authors: Prof. Dr. Suthep Suantai
• Format: Theses and Dissertations
• Language: English
• Published: เชียงใหม่ : บัณฑิตวิทยาลัย มหาวิทยาลัยเชียงใหม่ 2020
• Online Access: http://cmuir.cmu.ac.th/jspui/handle/6653943832/69521
• Institution: Chiang Mai University

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.