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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2023 / Volume: 52 Issue: 6

Error bounds for a class of history-dependent variational inequalities controlled by $\mathcal{D}$-gap~functions

Boling Chen(Yulin Normal University)0000-0002-1944-7975
Vo Minh Tam(Dong Thap University)0000-0002-3959-5449
Sayfa
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Yayın Tarihi
2023-11-03
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Finally, error bounds for the HDVI controlled by the regularized gap function and the $\mathcal{D}$-gap function are derived under suitable conditions.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In the present paper, we are concerned with investigating error bounds for history-dependent variational inequalities controlled by the difference gap (for brevity, $\mathcal{D}$-gap) functions.
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Temel Bulgular & Veri:First, we recall a class of elliptic variational inequalities involving the history-dependent operators (for brevity, HDVI).
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Sonuç & Katkı:Finally, error bounds for the HDVI controlled by the regularized gap function and the $\mathcal{D}$-gap function are derived under suitable conditions.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:History-dependent operator · Gap function · Error bound

Abstract

In the present paper, we are concerned with investigating error bounds for history-dependent variational inequalities controlled by the difference gap (for brevity, $\mathcal{D}$-gap) functions. First, we recall a class of elliptic variational inequalities involving the history-dependent operators (for brevity, HDVI). Then, we introduce a new concept of gap functions to the HDVI and propose the regularized gap function for the HDVI via the optimality condition for the concerning minimization problem. Consequently, the $\mathcal{D}$-gap function for the HDVI depends on these regularized gap functions is established. Finally, error bounds for the HDVI controlled by the regularized gap function and the $\mathcal{D}$-gap function are derived under suitable conditions.

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Bu Makaleye Atıf Yap

Chen, B., Tam, V. M. (2023). Error bounds for a class of history-dependent variational inequalities controlled by $\mathcal{D}$-gap~functions. Hacettepe Journal of Mathematics and Statistics, Volume: 52 Issue: 6. https://doi.org/10.15672/hujms.1183739

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