Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-682214220230201Convergence analysis and approximation of fixed point of multivalued generalized $\alpha$-nonexpansive mapping in uniformly convex Banach space4574683810.22075/ijnaa.2022.27791.3715ENUnwana UdofiaDepartment of Mathematics, Michael Okpara University of Agriculture, Umudike, Abia State, Nigeria0000-0002-8640-5804Donatus IkechiIgbokweDepartment of Mathematics, Michael Okpara University of Agriculture, Umudike, Abia State, Nigeria0000-0002-8574-6658Journal Article20220713Recently, the authors introduce a four-step iterative algorithm called the UD-iteration scheme (Udofia and Igbokwe [35]). Here we introduce the multivalued version of the UD-iteration scheme and show that it can be used to approximate the fixed points of multivalued contraction and multivalued generalized $\alpha$-nonexpansive mappings. we prove strong and weak convergence of the iteration scheme to the fixed point of multivalued generalized $\alpha$-nonexpansive mapping. We also prove that the scheme is $\varUpsilon$-stable and Data dependent. Convergence analysis shows that the multivalued UD-iteration scheme has a faster rate of convergence for multivalued contraction and multivalued generalized $\alpha$-nonexpansive mappings than some well-known existing iteration schemes in the literature.https://ijnaa.semnan.ac.ir/article_6838_b4ca3fbdb424cf723a3be4104b5bd6d2.pdf