Hybrid inertial accelerated algorithms for split fixed point problems of demicontractive mappings and equilibrium problems. (English) Zbl 1450.65048
Summary: Our contribution in this paper, we introduce and analyze two new hybrid algorithms by combining Mann iteration and inertial method for solving split fixed point problems of demicontractive mappings and equilibrium problems in a real Hilbert space. By using a new technique of choosing step size, our algorithms do not need any prior information on the operator norm. In fact, an inertial type algorithm was proposed in order to accelerate its convergence rate. We then prove weak and strong convergence of proposed methods under some control conditions. Moreover, some numerical experiments for image restoration problems and oligopolistic market equilibrium problems are also provided for supporting our main results.
MSC:
| 65J20 | Numerical solutions of ill-posed problems in abstract spaces; regularization |
| 65J22 | Numerical solution to inverse problems in abstract spaces |
| 65D18 | Numerical aspects of computer graphics, image analysis, and computational geometry |
Keywords:
demicontractive mappings; inertial method; split fixed point problem; equilibrium problem; Hilbert spacesReferences:
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