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Existence results for vector variational inequality problems on Hadamard manifolds

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Abstract

In this paper, we introduce and study vector variational inequality problems (VVIP) on Hadamard manifolds. The concepts of C-pseudomonotone, v-hemicontinuous and v-coercive operators are given. Some existence results for VVIP are obtained with the assumptions of C-pseudomonotonicity and v-hemicontinuity. These new results extend some corresponding known results given in literatures.

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Acknowledgements

The author is grateful to the editor and the referees for their valuable comments and suggestions. This work was supported by Chongqing Research Program of Basic Research and Frontier Technology (No. cstc2018jcyjAX0605), Scientific and Technological Research Program of Chongqing Municipal Education Commission (No. KJ1600433), and Foundation of Chongqing University of Posts and Telecommunications for the Scholars with Doctorate (No. A2015-19).

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Correspondence to Sheng-lan Chen.

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Chen, Sl. Existence results for vector variational inequality problems on Hadamard manifolds. Optim Lett 14, 2395–2411 (2020). https://doi.org/10.1007/s11590-020-01562-7

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