AN ERGODIC THEOREM FOR ASYMPTOTICALLY NONEXPANSIVE MAPPINGS IN CAT(0) SPACES

Hadi Khatibzadeh†

Abstract: In the framework of CAT(0) spaces, we prove that the mean of iterations of an asymptotically nonexpansive mapping with nonempty fixed point set converges weakly to a fixed point. The result extends the similar previous result for nonexpansive mappings in CAT(0) spaces [13] and generalizes the results of [11] from Hilbert spaces to Hadamard spaces.

Keywords: asymptotically nonexpansive, ergodic theorem, weak convergence, fixed point, CAT(0) space, Hadamard space.

MSC: 47H25, 47J25, 40A05.

DOI       10.56082/annalsarscimath.2026.2.95

Read full articleDYNAMICS OF THE ΛCDM MODEL OF THE UNIVERSE FROM THE PERSPECTIVE OF THE DYNAMICAL SYSTEMS THEORY                                                                                                                         Download articleDYNAMICS OF THE ΛCDM MODEL OF THE UNIVERSE FROM THE PERSPECTIVE OF THE DYNAMICAL SYSTEMS THEORY 

†hkhatibzadeh@znu.ac.ir, Department of Mathematics, University of Zanjan, Zanjan, Iran

PUBLISHED in

Annals Academy of Romanian Scientists Series on Mathematics and Its Application,

Volume 18 no 2, 2026

       

ISSN ONLINE 2066 – 6594
ISSN PRINT 2066 – 5997