Algorithms for Solving Resolvent of the Sum of Two Maximal Monotone Operators with Finite Family of Nonexpansive Operators

In this research paper, we address a variational problem using maximal monotone operators in conjunction with a finite family of nonexpansive operators. We propose a single-valued mapping whose fixed point allows us to find the solution to the main problem. Subsequently, we propose two algorithms. In the first, we introduce a system of sequences whose limit helps in solving the problem. In the second, we apply the Ishikawa algorithm to our setting using fixed point theory, which enables us to achieve strong convergence. Finally, we provide an illustrative example to demonstrate the applicability of our results.