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Paper IPM / M / 16969  


Abstract:  
In this paper, we study the problem of finding a common element
of the set of solutions of a system of monotone inclusion problems and the set
of common fixed points of a finite family of generalized demimetric mappings
in Hilbert spaces. We propose a new and efficient algorithm for solving this
problem. Our method relies on the inertial algorithm, Tsengâs splitting algorithm and the viscosity algorithm. Strong convergence analysis of the proposed method is established under standard and mild conditions. As applications we use our algorithm for finding the common solutions to variational inequality problems, the constrained multipleset split convex feasibility problem, the convex minimization problem and the common minimizer problem. Finally, we give some numerical results to show that our proposed algorithm is efficient and implementable from the numerical point of view.
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