Victor A. Uzor, Timilehin O. Alakoya, Oluwatosin T. Mewomo, Modified forward-backward splitting method for split equilibrium, variational inclusion, and fixed point problems
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Volume 5, Issue 1, 1 April 2023, Pages 95-119
Abstract. In the recent time, the problem of finding common solutions of fixed point problems (FPPs) of nonlinear mappings and optimization problems (OPs) has received great research attention due to its potential applications to mathematical models whose constraints can be expressed as the FPPs and OPs. In this paper, we study the problem of finding a common solution of a split equilibrium problem (SEP), a variational inclusion problem (VIP) and the FPP with a finite family of multivalued demicontractive mappings. We propose a new inertial iterative method, which employs the forward-backward splitting technique together with the viscosity method for approximating the solution of the problem in Hilbert spaces. The proposed method uses variable step sizes, which do not depend on the norm of the bounded linear operator. We prove strong convergence results under some mild conditions. Finally, we present some numerical experiments to demonstrate the efficiency and applicability of the proposed method. Our result improves and extends several existing results in the current literature in this direction.
How to Cite this Article:
V.A. Uzor, T.O. Alakoya, O.T. Mewomo, Modified forward-backward splitting method for split equilibrium, variational inclusion, and fixed point problems, Appl. Set-Valued Anal. Optim. 5 (2023), 95-119.