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arXiv · 2208.07126

Levitin-Polyak Well-posedness for Split Equilibrium Problems

Soumitra Dey·Aviv Gibali·Simeon Reich
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Abstract

The notion of well-posedness has drawn the attention of many researchers in the field of nonlinear analysis, as it allows to explore problems in which exact solutions are not known and/or computationally hard to compute. Roughly speaking, for a given problem, well-posedness guarantees the convergence of approximations to exact solutions via an iterative method. Thus, in this paper we extend the concept of Levitin-Polyak well-posedness to split equilibrium problems in real Banach spaces. In particular, we establish a metric characterization of Levitin-Polyak well-posedness by perturbations and also show an equivalence between Levitin-Polyak well-posedness by perturbations for split equilibrium problems and the existence and uniqueness of their solutions.

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Soumitra Dey, Aviv Gibali, Simeon Reich. 2022-08-15. Levitin-Polyak Well-posedness for Split Equilibrium Problems. https://doi.org/10.1007/s13398-023-01416-8

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