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A Mean Ergodic Theorem for Nonexpansive Mappings in Hadamard Spaces

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Abstract

In this paper, we prove a mean ergodic theorem for nonexpansive mappings in Hadamard (nonpositive curvature complete metric) spaces, which extends the Baillon nonlinear ergodic theorem. The main result shows that the sequence given by the Karcher means of iterations of a nonexpansive mapping with a nonempty fixed point set converges weakly to a fixed point of the mapping. This result also remains true for a 1-parameter continuous semigroup of contractions.

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  1. Department of Mathematics, University of Zanjan, P.O. Box 45195-313, Zanjan, 45371-38791, Iran

    H. Khatibzadeh & H. Pouladi

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  1. H. Khatibzadeh
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  2. H. Pouladi
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Correspondence to H. Khatibzadeh.

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Khatibzadeh, H., Pouladi, H. A Mean Ergodic Theorem for Nonexpansive Mappings in Hadamard Spaces. Anal Math 47, 329–342 (2021). https://doi.org/10.1007/s10476-021-0080-z

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  • DOI: https://doi.org/10.1007/s10476-021-0080-z

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