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A new method for solving split variational inequality problems without co-coerciveness

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Abstract

In solving the split variational inequality problems in real Hilbert spaces, the co-coercive assumption of the underlying operators is usually required and this may limit its usefulness in many applications. To have these operators freed from the usual and restrictive co-coercive assumption, we propose a method for solving the split variational inequality problem in two real Hilbert spaces without the co-coerciveness assumption on the operators. We prove that the proposed method converges strongly to a solution of the problem and give some numerical illustrations of it in comparison with other methods in the literature to support our strong convergence result.

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Acknowledgements

The authors sincerely thank the anonymous referees for their careful reading, constructive comments and fruitful suggestions that substantially improved the manuscript. The research of the first author is wholly supported by the National Research Foundation (NRF) South Africa (S& F-DSI/NRF Free Standing Postdoctoral Fellowship; Grant number: 120784). The first author also acknowledges the financial support from DSI/NRF, South Africa Center of Excellence in Mathematical and Statistical Sciences (CoE-MaSS) Postdoctoral Fellowship. The second author acknowledges the bursary and financial support from Department of Science and Innovation and National Research Foundation, Republic of South Africa Center of Excellence in Mathematical and Statistical Sciences (DSI-NRF COE-MaSS) Doctoral Bursary. The third author is supported by the NRF of South Africa Incentive Funding for Rated Researchers (Grant number 119903). Opinions expressed and conclusions arrived are those of the authors and are not necessarily to be attributed to NRF or CoE-MaSS.

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Authors and Affiliations

  1. School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa

    C. Izuchukwu, A. A. Mebawondu & O. T. Mewomo

  2. DSI-NRF Center of Excellence in Mathematical and Statistical Sciences (CoE-MaSS), Johannesburg, South Africa

    A. A. Mebawondu

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  1. C. Izuchukwu
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  2. A. A. Mebawondu
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  3. O. T. Mewomo
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Correspondence to O. T. Mewomo.

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Izuchukwu, C., Mebawondu, A.A. & Mewomo, O.T. A new method for solving split variational inequality problems without co-coerciveness. J. Fixed Point Theory Appl. 22, 98 (2020). https://doi.org/10.1007/s11784-020-00834-0

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