Global error bounds for mixed Quasi-Hemivariational inequality problems on Hadamard manifolds

ABSTRACT

In this paper, we introduce and study a class of mixed quasi-hemivariational inequality problems on Hadamard manifolds (in short, (MQHIP)). Some regularized gap functions for (MQHIP) are proposed under suitable conditions. Finally, global error bounds for (MQHIP) in terms of regularized gap functions are derived by employing some strong monotonicity conditions and using the properties of Clarke's generalized directional derivative. The main results presented in this paper improve and generalize corresponding results in literature.

Keywords:

• Mixed quasi-hemivariational inequality
• regularized gap function
• global error bound
• Hadamard manifold

2010 Mathematics Subject Classifications:

• 47J20
• 49J40

Acknowledgments

The authors are grateful to the Editor and the Reviewers for their valuable remarks which improved the results and presentation of this article.

Disclosure statement

No potential conflict of interest was reported by the authors.