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Existence of solutions for extended generalized complementarity problems

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Abstract

In this paper we introduce extended generalized complementarity problems in Hausdorff topological vector spaces in duality and study the existence of their solutions. We use a different method than those in literature on the existence of solutions of complementarity problems, which are usually based on arguments from generalized monotonicity. This leads us to obtain new results and improve many existing results in literature. We also prove some existence results for extended generalized complementarity problems in reflexive Banach spaces by means of a Tikhonov regularization procedure under a copositivity assumption and arguments from the recession analysis.

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Acknowledgements

The authors would like to thank the Associate Editor and the anonymous referee for their valuable comments and suggestions which helped us very much in improving the original version of this paper. The first author wishes to thank the UGC (University Grants Commission), New Delhi, India for the grant of research fellowship (UGC-F.2-4/2013(SA-I)) and IIT Bhubaneswar for providing research facilities. The second author was partially supported by the Fulbright fellowship during his visit to the department of Mathematics of the University of Central Florida. The third author is grateful to the Mohapatra Family Foundation for it’s support during the finale stages of this research.

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Authors and Affiliations

  1. School of Basic Sciences, Indian Institute of Technology Bhubaneswar, Bhubaneswar, 752050, India

    Bijaya Kumar Sahu & Sabyasachi Pani

  2. Department of Economics, Faculty of Economics and Social Sciences, Ibn Zohr University, B.P. 8658, Poste Dakhla, Agadir, Morocco

    Ouayl Chadli

  3. Department of Mathematics, University of Central Florida, Orlando, FL, USA

    Ram N. Mohapatra

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  1. Bijaya Kumar Sahu
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  2. Ouayl Chadli
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  4. Sabyasachi Pani
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Correspondence to Ouayl Chadli.

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Sahu, B.K., Chadli, O., Mohapatra, R.N. et al. Existence of solutions for extended generalized complementarity problems. Positivity 25, 769–789 (2021). https://doi.org/10.1007/s11117-020-00786-2

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