Self-adaptive forward–backward splitting algorithm for the sum of two monotone operators in Banach spaces

Abstract

Abstract In this work, we prove the weak convergence of a one-step self-adaptive algorithm to a solution of the sum of two monotone operators in 2-uniformly convex and uniformly smooth real Banach spaces. We give numerical examples in infinite-dimensional spaces to compare our result with some existing algorithms. Finally, our results extend and complement several existing results in the literature.

Keywords

• Maximal monotone operators
• Lipschitz-continuous operator
• Forward–reflected–backward splitting method
• 2-uniformly convex spaces