Open AccessAn evolution equation governed by a quasi-nonexpansive mapping on Hadamard manifolds and its backward discretization
Author(s) -
Hadi Khatibzadeh,
M. Rahimi
Publication year - 2020
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2007217k
Subject(s) - mathematics , discretization , hadamard transform , lipschitz continuity , fixed point , infinity , mathematical analysis
We study the asymptotic behavior of solutions to a first-order evolution equation governed by a locally Lipschitz quasi-nonexpansive mapping. We show that such solutions converge to a fixed point of the quasi-nonexpansive mapping as time goes to infinity. Time discretization of this system provides an iterative method to approximate a fixed point of quasi-nonexpansive mappings on Hadamard manifolds.