Iterative manner involving sunny nonexpansive retractions for nonlinear operators from the perspective of convex programming as applicable to differential problems, image restoration and signal recovery

Abstract

In this paper, using sunny nonexpansive retractions which are different from the metric projection in Banach spaces, we develop the CR-iteration algorithm in view of two quasi-nonexpansive nonself mappings and also give the convergence analysis for the proposed method in the setting of uniformly convex Banach spaces. Furthermore, our results can be applied for the purpose of finding common zeros of accretive operators, convexly constrained least square problems and convex minimization problems. Regarding application, some numerical experiments involving real-world problems are provided, with focus on differential problems, image restoration problems and signal recovery problems.

Keywords

• convexly constrained least square problem
• convex minimization problem
• signal recovery problem
• image restoration problem
• sunny nonexpansive retract