Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 14 2 2023 02 01 Convergence analysis and approximation of fixed point of multivalued generalized $\alpha$-nonexpansive mapping in uniformly convex Banach space 45 74 6838 10.22075/ijnaa.2022.27791.3715 EN Unwana Udofia Department of Mathematics, Michael Okpara University of Agriculture, Umudike, Abia State, Nigeria Donatus Ikechi Igbokwe Department of Mathematics, Michael Okpara University of Agriculture, Umudike, Abia State, Nigeria Journal Article 2022 07 13 Recently, 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