Composite iterative schemes for maximal monotone operators in reflexive Banach spaces

Abstract

Abstract In this article, we introduce composite iterative schemes for finding a zero point of a finite family of maximal monotone operators in a reflexive Banach space. Then, we prove strong convergence theorems by using a shrinking projection method. Moreover, we also apply our results to a system of convex minimization problems in reflexive Banach spaces. AMS Subject Classification: 47H09, 47H10

Keywords

• Maximal monotone operator
• Shrinking projection method
• Proximal point algorithm
• Bregman projection
• Totally convex function
• Legendre function