# Well-posedness for generalized variational-hemivariational inequalities with perturbations in reflexive banach spaces

## DOI:

https://doi.org/10.5556/j.tkjm.48.2017.2460## Keywords:

Generalized variational-hemivariational inequality, Well-posedness, Clarke's generalized gradient, Approximating sequence, Inclusion problem## Abstract

In this paper, we consider an extension of well-posedness for a minimization problem to a class of generalized variational-hemivariational inequalities with perturbations in reflexive Banach spaces. We establish some metric characterizations for the $\alpha$-well-posed generalized variational-hemivariational inequality and give some conditions under which the generalized variational-hemivariational inequality is strongly $\alpha$-well-posed in the generalized sense. Under some mild conditions, we also prove the equivalence between the $\alpha$-well-posedness of the generalized variational-hemivariational inequality and the $\alpha$-well-posedness of the corresponding inclusion problem.## References

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*Tamkang Journal of Mathematics*,

*48*(4), 345–364. https://doi.org/10.5556/j.tkjm.48.2017.2460