Convergence analysis and approximation of fixed point of multivalued generalized \alpha-nonexpansive mapping in uniformly convex Banach space

Recently, the authors introduce a four-step iterative algorithm called the UD-iteration scheme (Udofia and Igbokwe [۳۵]). 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.

کلیدواژه ها:

uniformly convex Banach space ، Multivalued generalized \alpha-nonexpansive Mapping ، convergence ، data dependence ، stability