In this work, we first introduce the modified S-iteration method to approximate common fixed points of three multi-valued generalized $( \alpha -\beta )$-nonexpansive mappings in the setting of Banach spaces. Then we prove some convergence theorems for these mappings by using it. Also, a numerical example is given to illustrate the main results. Furthermore, we introduce a one-step iterative process for generalized $( \alpha -\beta )$-nonexpansive mappings and we prove strong convergence results for the one-step iterative process involving such mappings. Thus our results extend and generalise corresponding results in the contemporary literature.
Karaca,N . (2023). Convergence of the S-iteration process for the multi-valued generalized $( \alpha -\beta )$-nonexpansive mappings in Banach spaces. International Journal of Nonlinear Analysis and Applications, 14(1), 2007-2018. doi: 10.22075/ijnaa.2022.25721.3107
MLA
Karaca,N . "Convergence of the S-iteration process for the multi-valued generalized $( \alpha -\beta )$-nonexpansive mappings in Banach spaces", International Journal of Nonlinear Analysis and Applications, 14, 1, 2023, 2007-2018. doi: 10.22075/ijnaa.2022.25721.3107
HARVARD
Karaca N. (2023). 'Convergence of the S-iteration process for the multi-valued generalized $( \alpha -\beta )$-nonexpansive mappings in Banach spaces', International Journal of Nonlinear Analysis and Applications, 14(1), pp. 2007-2018. doi: 10.22075/ijnaa.2022.25721.3107
CHICAGO
N Karaca, "Convergence of the S-iteration process for the multi-valued generalized $( \alpha -\beta )$-nonexpansive mappings in Banach spaces," International Journal of Nonlinear Analysis and Applications, 14 1 (2023): 2007-2018, doi: 10.22075/ijnaa.2022.25721.3107
VANCOUVER
Karaca N. Convergence of the S-iteration process for the multi-valued generalized $( \alpha -\beta )$-nonexpansive mappings in Banach spaces. IJNAA. 2023;14(1):2007-2018. doi: 10.22075/ijnaa.2022.25721.3107
International Journal of Nonlinear Analysis and Applications