convergence analysis and approximation of fixed point of multivalued generalized α-nonexpansive mapping in uniformly convex banach space

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 α-nonexpansive mappings. we prove strong and weak convergence of the iteration scheme to the fixed point of multivalued generalized α-nonexpansive mapping. we also prove that the scheme is υ-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 α-nonexpansive mappings than some well-known existing iteration schemes in the literature.