Existence and Computational Approximation of Fixed Points of Generalized Multivalued Mappings in Banach Space

In this chapter, we introduce the multivalued version of a recently proposed nonexpansive mapping in a uniformly convex Banach space. We explore the properties and applications of this new multivalued generalized \((\tilde{\alpha }, \tilde{\beta }, \tilde{\gamma })-\) nonexpansive mapping. We also present the convergence results for the Picard–Thakur hybrid iterative scheme. Through numerical and graphical analysis, we demonstrate that the Picard–Thakur hybrid iterative scheme converges at a faster rate compared to other schemes. Additionally, we provide an application that establishes a connection between our results and real-world phenomena.