On error bounds for fixed point problems and its applications

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This research aims to develop efficient algorithms for solving fixed point problems. Especially, we investigated notions that guarantee sequences generated by iterative methods can obtain an exact solution in finite number of steps. First, we provided a new condition for set-valued mappings based on theoretical techniques for solving the convex programming problem. Further, by using these results, we derived finite convergence results concerning nonlinear problems such as the convex minimization problem and the variational inequality.