New Parallel Fixed Point Algorithms and Their Application to a System of Variational Inequalities

Abstract

In this study, considering the advantages of parallel fixed point algorithms arising from their symmetrical behavior, new types of parallel algorithms have been defined. Strong convergence of these algorithms for certain mappings with altering points has been analyzed, and it has been observed that their convergence behavior is better than existing algorithms with non-simple samples. In addition, the concept of data dependency for these algorithms has been examined for the first time in this study. Finally, it has been proven that the solution of a variational inequality system can be obtained using newly defined parallel algorithms under suitable conditions.

Keywords

• iterative algorithm
• variational inequalities
• relaxed (<i>κ</i>, <i>ω</i>)-cocoercive mappings
• nonexpansive mappings