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

  • C. Izuchukwu
  • A. A. Mebawondu
  • K. O. Aremu
  • H. A. Abass
  • O. T. MewomoEmail author
Article
  • 13 Downloads

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.

Keywords

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

Mathematics Subject Classification

47H09 47H10 49J20 49J40 

Notes

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.

Compliance with ethical standards

Conflicts of interest

The authors declare that they have no competing interests.

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Copyright information

© Springer-Verlag Italia S.r.l., part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mathematics, Statistics and Computer ScienceUniversity of KwaZulu-NatalDurbanSouth Africa

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