Forward-reflected-backward splitting method without cocoercivity for the sum of maximal monotone operators in Banach spaces

Abstract

Let E be a real 2-uniformly convex Banach space with topological dual $E^{\ast }$. We prove weak convergence of the forward-reflected-backward splitting method to a solution of inclusion of sum of two monotone operators. Moreover, we give a variant of the method in which the step size does not depend on the Lipschitz constant of one of the operators. Finally, our results extend and complement several existing results in the literature. We also give some numerical illustrations of the proposed method in comparison with other method in the literature to further demonstrate the applicability and efficiency of our method.

Keywords:

• Maximally monotone operators
• Lipschitz-continuous operator
• forward-reflected-backward splitting method
• 2-uniformly convex spaces

2000 Mathematics Subject Classifications:

• 47H09
• 47H10
• 49J20
• 49J40

Disclosure statement

No potential conflict of interest was reported by the author(s).