Malaysian Journal of Mathematical Sciences, September 2026, Vol. 20, No. 3
Approximating Fixed Points of Multi-Valued Generalized Nonexpansive Mappings with Applications
Yadav, S. and Chamola, B. P.
Corresponding Email: suchetaydv@gmail.com
Received date: 9 September 2025
Accepted date: 22 January 2026
Abstract:
In this paper, we extend the concept of generalized $(\alpha,\beta)-$ nonexpansive type 1 mappings to the multivalued setting. We establish several fundamental properties of mappings of this class and derive fixed point existence results under suitable assumptions in Banach spaces. To approximate their common fixed points in the context of Banach spaces, we give a multivalued variant of the M-iterative process. The convergence and stability results are establish, supported by illustrative numerical examples. These results broaden the scope of iterative approximation techniques and contribute to the growing theory of multi-valued nonexpansive-type mappings. The study further includes an application to Volterra-type integral inclusions.
Keywords: common fixed point, uniformly convex Banach space, strong convergence, stability.
