Bulletin of the Belgian Mathematical Society - Simon Stevin

A viscosity iterative algorithm for a family of monotone inclusion problems in an Hadamard space

G.N. Ogwo, C. Izuchukwu, K.O. Aremu, and O.T. Mewomo

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

In this paper, we introduce a viscosity-type proximal point algorithm which comprises of a finite sum of resolvents of monotone operators, and a generalized asymptotically nonexpansive mapping. We prove that the algorithm converges strongly to a common zero of a finite family of monotone operators, which is also a fixed point of a generalized asymptotically nonexpansive mapping in an Hadamard space. Furthermore, we give two numerical examples of our algorithm in finite dimensional spaces of real numbers and one numerical example in a non-Hilbert space setting, in order to show the applicability of our results.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 27, Number 1 (2020), 127-152.

Dates
First available in Project Euclid: 23 May 2020

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1590199308

Digital Object Identifier
doi:10.36045/bbms/1590199308

Mathematical Reviews number (MathSciNet)
MR4102705

Zentralblatt MATH identifier
07213662

Subjects
Primary: 47H09: Contraction-type mappings, nonexpansive mappings, A-proper mappings, etc. 47H10: Fixed-point theorems [See also 37C25, 54H25, 55M20, 58C30] 49J20: Optimal control problems involving partial differential equations 49J40: Variational methods including variational inequalities [See also 47J20]

Keywords
CAT(0) spaces monotone inclusion problem monotone operators generalized asymptotically nonexpansive variational inequalities

Citation

Ogwo, G.N.; Izuchukwu, C.; Aremu, K.O.; Mewomo, O.T. A viscosity iterative algorithm for a family of monotone inclusion problems in an Hadamard space. Bull. Belg. Math. Soc. Simon Stevin 27 (2020), no. 1, 127--152. doi:10.36045/bbms/1590199308. https://projecteuclid.org/euclid.bbms/1590199308


Export citation