General-type proximal point algorithm for solving inclusion and fixed point problems with composite operators | ||||
| Journal of the Egyptian Mathematical Society | ||||
| Volume 28, Issue 1, June 2020, Page 1-17 PDF (471.16 K) | ||||
| DOI: 10.1186/s42787-020-00080-w | ||||
 View on SCiNiTO | ||||
| Author | ||||
| T. M. M. Sow | ||||
| Gaston Berger University, Saint Louis, Senegal | ||||
| Abstract | ||||
| The main purpose of this paper is to introduce a new general-type proximal point algorithm for finding a common element of the set of solutions of monotone inclusion problem, the set of minimizers of a convex function, and the set of solutions of fixed point problem with composite operators: the composition of quasi-nonexpansive and firmly nonexpansive mappings in real Hilbert spaces. We prove that the sequence xn which is generated by the proposed iterative algorithm converges strongly to a common element of the three sets above without commuting assumption on the mappings. Finally, applications of our theorems to find a common solution of some nonlinear problems, namely, composite minimization problems, convex optimization problems, and fixed point problems, are given to validate our new findings. | ||||
| Keywords | ||||
| General-type proximal algorithm; Convex minimization problem; Monotone inclusion problem; Composite operators | ||||
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