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.
M. Sow, T. (2020). General-type proximal point algorithm for solving inclusion and fixed point problems with composite operators. Journal of the Egyptian Mathematical Society, 28(1), 1-17. doi: https://doi.org/10.1186/s42787-020-00080-w
MLA
T. M. M. Sow. "General-type proximal point algorithm for solving inclusion and fixed point problems with composite operators", Journal of the Egyptian Mathematical Society, 28, 1, 2020, 1-17. doi: https://doi.org/10.1186/s42787-020-00080-w
HARVARD
M. Sow, T. (2020). 'General-type proximal point algorithm for solving inclusion and fixed point problems with composite operators', Journal of the Egyptian Mathematical Society, 28(1), pp. 1-17. doi: https://doi.org/10.1186/s42787-020-00080-w
VANCOUVER
M. Sow, T. General-type proximal point algorithm for solving inclusion and fixed point problems with composite operators. Journal of the Egyptian Mathematical Society, 2020; 28(1): 1-17. doi: https://doi.org/10.1186/s42787-020-00080-w
)
