Abstract
AbstractWe propose a hybrid inertial self-adaptive algorithm for solving the split feasibility problem and fixed point problem in the class of demicontractive mappings. Our results are very general and extend several related results existing in the literature from the class of nonexpansive or quasi-nonexpansive mappings to the larger class of demicontractive mappings. Examples to illustrate numerically the effectiveness of the new analytical results are presented.
Publisher
Springer Science and Business Media LLC
Reference21 articles.
1. Berinde, V.: Approximating fixed points of enriched nonexpansive mappings in Banach spaces by using a retraction-displacement condition. Carpath. J. Math. 36(1), 27–34 (2020)
2. Berinde, V.: A modified Krasnoselskii-Mann iterative algorithm for approximating fixed points of enriched nonexpansive mappings. Symmetry 14(1), 123 (2022). https://doi.org/10.3390/sym14010123
3. Berinde, V.: Approximating fixed points of demicontractive mappings via the quasi-nonexpansive case. Carpath. J. Math. 39(1), 73–85 (2023)
4. Berinde, V.: On a useful lemma that relates quasi-nonexpansive and demicontractive mappings in Hilbert spaces. Creative Math. Inform. 33(1), 7–21 (2024)
5. Berinde, V., Petruşel, A., Rus, I.A.: Remarks on the terminology of the mappings in fixed point iterative methods in metric spaces. Fixed Point Theory 24(2), 525–540 (2023)