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Stability analysis of set-valued inverse variational inequalities in reflexive Banach spaces

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Abstract

In this paper, a new class of set-valued inverse variational inequalities (SIVIs) are introduced and investigated in reflexive Banach spaces. Several equivalent characterizations are given for the set-valued inverse variational inequality to have a nonempty and bounded solution set. Based on the equivalent condition, we propose the stability result for the set-valued inverse variational inequality with both the mapping and the constraint set that are perturbed in a reflexive Banach space, provided that the mapping is monotone. Furthermore, some examples are shown to support the main results. The results in this paper generalize and extend some known results in this area.

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Authors and Affiliations

  1. Department of Mathematics, Southwest Minzu University, Chengdu, 610041, Sichuan, People’s Republic of China

    Xue-ping Luo

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  1. Xue-ping Luo
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Correspondence to Xue-ping Luo.

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The work was supported by National Natural Science Foundation of China (Grant 11701480), China Postdoctoral Science Foundation (Grant 2018M631072), Fundamental Research Funds for the Central Universities, Southwest Minzu University (Grant 2020NYBPY05), and Key Projects of the Education Department of Sichuan Province (Grant 18ZA0511).

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Luo, Xp. Stability analysis of set-valued inverse variational inequalities in reflexive Banach spaces. J. Fixed Point Theory Appl. 23, 41 (2021). https://doi.org/10.1007/s11784-021-00882-0

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