The super fixed point property for asymptotically nonexpansive mappings

Volume 217 / 2012

Andrzej Wiśnicki Fundamenta Mathematicae 217 (2012), 265-277 MSC: Primary 47H09, 47H10; Secondary 46B08. DOI: 10.4064/fm217-3-5

Abstract

We show that the super fixed point property for nonexpansive mappings and for asymptotically nonexpansive mappings in the intermediate sense are equivalent. As a consequence, we obtain fixed point theorems for asymptotically nonexpansive mappings in uniformly nonsquare and uniformly noncreasy Banach spaces. The results are generalized to commuting families of asymptotically nonexpansive mappings.

Authors

  • Andrzej WiśnickiInstitute of Mathematics
    Maria Curie-Skłodowska University
    20-031 Lublin, Poland
    e-mail

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