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Fixed point theorems for a class of nonlinear mappings related to maximal monotone operators in Banach spaces

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Abstract.

In this paper, the class of nonspreading mappings in Banach spaces is introduced. This class contains the recently introduced class of firmly nonexpansive type mappings in Banach spaces and the class of firmly nonexpansive mappings in Hilbert spaces. Among other things, we obtain a fixed point theorem for a single nonspreading mapping in Banach spaces. Using this result, we also obtain a common fixed point theorem for a commutative family of nonspreading mappings in Banach spaces.

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Correspondence to Fumiaki Kohsaka.

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Received: 10 August 2007

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Kohsaka, F., Takahashi, W. Fixed point theorems for a class of nonlinear mappings related to maximal monotone operators in Banach spaces. Arch. Math. 91, 166–177 (2008). https://doi.org/10.1007/s00013-008-2545-8

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Mathematics Subject Classification (2000).

  • Primary 47H10
  • Secondary 47H05

Keywords.

  • Firmly nonexpansive mapping
  • firmly nonexpansive type mapping
  • fixed point theorem
  • nonspreading mapping
  • resolvent of monotone operator