@article{Ji2024, 
author = {Dong Ji and Yao Yu and Chaobo Li},
title = {Fixed point and endpoint theorems of multivalued mappings in convex    b-metric spaces with an application},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {3},
pages = {7589-7609},
keywords = {fixed point and endpoint, multivalued α-nonexpansive mapping, S-iterative process, b-metric space, quadratic integral equation},
url = {https://www.sciopen.com/article/10.3934/math.2024368},
doi = {10.3934/math.2024368},
abstract = {In this paper, we investigated several new fixed points theorems for multivalued mappings in the framework    b-metric spaces. We first generalized    S-iterative schemes for multivalued mappings to above spaces by means of a convex structure and then we developed the existence of fixed points and approximate endpoints of the multivalued contraction mappings using iteration techniques. Furthermore, we introduced the modified    S-iteration process for approximating a common endpoint of a multivalued        α          s      -nonexpansive mapping and a multivalued mapping satisfying conditon    (      E                          ′              ). We also showed that this new iteration process converges faster than the    S-iteration process in the sense of Berinde. Some convergence results for this iterative procedure to a common endpoint under some certain additional hypotheses were proved. As an application, we applied the    S-iteration process in finding the solution to a class of nonlinear quadratic integral equations.}
}