DOI: 10.3390/sym16040483 ISSN: 2073-8994

Common Fixed-Point Theorem and Projection Method on a Hadamard Space

Yasunori Kimura
  • Physics and Astronomy (miscellaneous)
  • General Mathematics
  • Chemistry (miscellaneous)
  • Computer Science (miscellaneous)

In this paper, we obtain an equivalent condition to the existence of a common fixed point of a given family of nonexpansive mappings defined on a Hadamard space. Moreover, if the space is bounded, we show that the generating process of the approximate sequence by a specific projection method will stop in finite steps if there is no common fixed point. It is a significant advantage to reveal the nonexistence of a common fixed point in a finite time.

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