Well-posedness for the split equilibrium problem

Soumitra Dey; V. Vetrivel; Hong-Kun Xu

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arXiv · 2305.02696

Well-posedness for the split equilibrium problem

Soumitra Dey·V. Vetrivel·Hong-Kun Xu

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Abstract

We extend the concept of well-posedness to the split equilibrium problem and establish Furi-Vignoli-type characterizations for the well-posedness. We prove that the well-posedness of the split equilibrium problem is equivalent to the existence and uniqueness of its solution under certain assumptions on the bifunctions involved. We also characterize the generalized well-posedness of the split equilibrium problem via the Kuratowski measure of noncompactness. We illustrate our theoretical results by several examples.

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Soumitra Dey, V. Vetrivel, Hong-Kun Xu. 2023-05-04. Well-posedness for the split equilibrium problem. https://arxiv.org/abs/2305.02696

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