An evolution equation governed by a quasi-nonexpansive mapping on Hadamard manifolds and its backward discretization | Zendy

Hadi Khatibzadeh | Zendy; Mohsen Rahimi Piranfar | Zendy

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An evolution equation governed by a quasi-nonexpansive mapping on Hadamard manifolds and its backward discretization

Author(s) -

Hadi Khatibzadeh,

Mohsen Rahimi Piranfar

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.

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