In this paper, a new modified proximal point algorithm involving fixed point of nonspreading-type multivalued mappings in Hilbert spaces is proposed. Under suitable conditions, some weak convergence and strong convergence to a common element of the set of minimizers of a convex function and the set of fixed points of the nonspreading-type multivalued mappings in Hilbert space are proved. The presented results in the paper are new.
In this paper, we introduce and study the strong convergence problem of the improved Ishikawa iteration with error correction for Lipschitzian and demi-contraction semi-groups in a general Banach spaces. The obtained results in this paper extend and improve some recent results in other papers.
In this paper, the convergence to minimizers of a convex function of a modified proximal point algorithm involving a single-valued nonexpansive mapping and a multivalued nonexpansive mapping in CAT(0) spaces is studied and a numerical example is given to support our main results.
In this paper, we introduce the modified iterations of Mann's type for nonexpansive mapping and asymptotically nonexpansive mapping to have the strong and weak convergence in a uniformly convex Banach space. We also proved strong convergence theorems of our modified Mann's iteration processes for nonexpansive semigroups and asymptotically nonexpansive semigroups. The results presented in the paper give a partially affirmative answer to the open question raised by Kim and Xu (Nonlinear Anal. 64:1140-1152. Applications to the accretive operators are also included. MSC: 47H09; 47H10; 47J25
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.