Algorithms for Solving Split Equality Variational Inequality Problems Involving Quasi-monotone Mappings in Banach Spaces

Abstract

The main objective of this thesis is to introduce a more general problem called the Split Equality Variational Inequality Problems (SEVIP) and the Split Equality Duality Variational Inequality Problems (SEDVIP) and formulate algorithms which solve the SEVIP and SEDVIP involving quasi-monotone mappings in reflexive real Banach spaces. In order to solve this problem, we propose double projection like methods to approximate some solution of the SEVIP and SEDVIP. Using these methods, we prove weak and/or strong convergence of the algorithms to solutions of the variational inequality problems under mild conditions. In addition, we provide some applications of SEVIPs and SEDVIPs. We also present numerical examples to validate the application of the algorithm. The results reached in this thesis generalize and improve a number of results in the literature of this field.