Open Access Open Access  Restricted Access Subscription or Fee Access

Duality Theorems and Convergence Theorems for Nonlinear Mappings in Banach Spaces and Applications

Takashi Honda, Takanori Ibaraki, Wataru Takahashi

Abstract


In this paper, we first prove duality theorems for two classes of nonlinear mappings which are connected with resolvents of maximal monotone operators in Banach spaces. Two classes of nonlinear mappings are a relatively nonexpansive mapping and a generalized nonexpansive mapping. Then, we discuss the existence of sunny generalized nonexpansive mappings and the weak convergence of sequences generated by firmly generalized nonexpansive mappings in Banach spaces. Finally, we apply these results to conditional expectations in the probability theory.

Full Text:

PDF


Disclaimer/Regarding indexing issue:

We have provided the online access of all issues and papers to the indexing agencies (as given on journal web site). It’s depend on indexing agencies when, how and what manner they can index or not. Hence, we like to inform that on the basis of earlier indexing, we can’t predict the today or future indexing policy of third party (i.e. indexing agencies) as they have right to discontinue any journal at any time without prior information to the journal. So, please neither sends any question nor expects any answer from us on the behalf of third party i.e. indexing agencies.Hence, we will not issue any certificate or letter for indexing issue. Our role is just to provide the online access to them. So we do properly this and one can visit indexing agencies website to get the authentic information.