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

Takashi Honda, Takanori Ibaraki, Wataru Takahashi


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.

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