Bulletin of the Belgian Mathematical Society - Simon Stevin
- Bull. Belg. Math. Soc. Simon Stevin
- Volume 27, Number 1 (2020), 127-152.
A viscosity iterative algorithm for a family of monotone inclusion problems in an Hadamard space
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.
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]
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