Abstract
AbstractThe purpose of this paper is to propose a new inertial self-adaptive algorithm for generalized split system of common fixed point problems of finite family of averaged mappings in the framework of Hilbert spaces. The weak convergence theorem of the proposed method is given and its theoretical application for solving several generalized problems is presented. The behavior and efficiency of the proposed algorithm is illustrated by some numerical tests.
Publisher
Springer Science and Business Media LLC
Reference48 articles.
1. Abubakar, J., Kumam, P., Hassan Ibrahim, A., ur Rehman, H.: Inertial iterative schemes with variable step sizes for variational inequality problem involving pseudomonotone operator. Mathematics 8(4), 609 (2020)
2. Alvarez, F.; Attouch, H.: An inertial proximal method for maximal monotone operators via discretization of a nonlinear oscillator with damping. Set Val. Anal. 9(1–2), 3–11 (2001)
3. Bailion, J.; Bruck, R.E.; Reich, S.: On the asymptotic behavior of nonexpansive mappings and semigroups in Banach spaces. Houston J. Math. 4(3), 1–9 (1978)
4. Bauschke, H.H.: The approximation of fixed points of compositions of nonexpansive mappings in Hilbert space. J. Math. Anal. Appl. 202(1), 150–159 (1996)
5. Bauschke, H.H.; Combettes, P.L.; et al.: Convex Analysis and Monotone Operator Theory in Hilbert Spaces, vol. 408. Springer, New York (2011)