Convergence Analysis of Best Proximity Point Problems and Split Problems for Demicontractive Operators with Applications

Abstract

This dissertation consists of the two main results which are the study of best proximity point problems and split problems for demicontractive operators. To achieve the first result, we introduce a general Mann algorithm for nonself nonexpansive mappings and then prove weak and strong convergence of the proposed algorithm under some suitable conditions in Hilbert spaces. Furthermore, we also provide numerical experiments to illustrate the convergence behavior of our proposed algorithm. To achieve the second result, we construct three self-adaptive algorithms with inertial effects for solving the split problems for demicontractive operators. Under some suitable conditions, the weak and strong convergence of the algorithms are obtained. Numerical results of image restoration problems illustrate that these proposed algorithms are efficient and outperform other ones.