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We study the widely more generalized hybrid mappings which have been proposed to unify several well-known nonlinear mappings including the nonexpansive mappings, nonspreading mappings, hybridmappings, and generalized hybrid mappings. Without the convexity assumption, we will establish the existence theorem and mean convergence theoremfor attractive point of the widely more generalized hybrid mappings in a Hilbertspace. Moreover, we prove a weak convergence theorem of Mann’s type and astrong convergence theorem of Shimizu and Takahashi’s type for such a wideclass of nonlinear mappings in a Hilbert space. Our results can be viewed as ageneralization of Kocourek, Takahashi and Yao, and Hojo and Takahashi wherethey studied the generalized hybrid mappings

Existence and Approximation of Attractive Points of the Widely More Generalized Hybrid Mappings in Hilbert Spaces