Viscosity iterative techniques for approximating a common zero of monotone operators in an Hadamard space

Abstract

The main purpose of this paper is to introduce some viscosity-type proximal point algorithms which comprise of a nonexpansive mapping and a finite sum of resolvents of monotone operators, and prove their strong convergence to a common zero of a finite family of monotone operators which is also a fixed point of a nonexpansive mapping and a unique solution of some variational inequality problems in an Hadamard space. We apply our results to solve a finite family of convex minimization problems, variational inequality problems and convex feasibility problems.

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Acknowledgements

The fourth author acknowledge with thanks the bursary and financial support from Department of Science and Technology and National Research Foundation, Republic of South Africa Center of Excellence in Mathematical and Statistical Sciences (DST-NRF COE-MaSS) Doctoral Bursary. Opinions expressed and conclusions arrived are those of the authors and are not necessarily to be attributed to the CoE-MaSS.

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Correspondence to O. T. Mewomo.

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Izuchukwu, C., Mebawondu, A.A., Aremu, K.O. et al. Viscosity iterative techniques for approximating a common zero of monotone operators in an Hadamard space. Rend. Circ. Mat. Palermo, II. Ser 69, 475–495 (2020). https://doi.org/10.1007/s12215-019-00415-2

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Keywords

  • Monotone operators
  • Convex feasibility problems
  • Variational inequalities
  • Minimization problems
  • Viscosity iterations
  • CAT(0) space

Mathematics Subject Classification

  • 47H09
  • 47H10
  • 49J20
  • 49J40