Weak and Strong Mean Convergence Theorems for Super Hybrid Mappings in Hilbert Spaces

  title={Weak and Strong Mean Convergence Theorems for Super Hybrid Mappings in Hilbert Spaces},
  author={Mayumi Hojo and Wataru Takahashi and Jen-Chih Yao},
In this paper, we first introduce a class of nonlinear mappings called extended hybrid in a Hilbert space containing the class of generalized hybrid mappings. The class is different from the class of super hybrid mappings which was defined by Kocourek, Takahashi and Yao [12]. We prove a fixed point theorem for generalized hybrid nonself-mapping in a Hilbert space. Next, we prove a nonlinear ergodic theorem of Baillon’s type for super hybrid mappings in a Hilbert space. Finally, we deal with two… CONTINUE READING
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