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

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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

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

First available in Project Euclid: 23 May 2020

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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]

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


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

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