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Existence and boundedness of solutions to inclusion problems for maximal monotone vector fields in Hadamard manifolds

  • Qamrul Hasan AnsariEmail author
  • Feeroz Babu
Original Paper

Abstract

In this paper, we consider the inclusion problems for maximal monotone set-valued vector fields defined on Hadamard manifolds. We discuss the equivalence between nonemptiness of solution set of the inclusion problem and the coercivity condition. The boundedness of solution set of the inclusion problem is studied. An application of our results to optimization problems in Hadamard manifolds is also presented.

Keywords

Inclusion problems Maximal monotone vector fields Coercivity conditions Existence results Boundedness of solution set Hadamard manifolds 

Mathematics Subject Classification

49J40 47H05 47J20 49J53 51H25 90C33 

Notes

Acknowledgements

Authors are grateful to the references for their valuable suggestions and corrections. In this research, first author was supported by a research grant of DSR-SERB No. EMR/2016/005124.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsAligarh Muslim UniversityAligarhIndia
  2. 2.Department of Mathematics and StatisticsKing Fahd University of Petroleum and MineralsDhahranSaudi Arabia

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