Mixed vector equilibrium-like problems on Hadamard manifolds: error bound analysis

Abstract

In this paper, we introduce and investigate mixed vector equilibrium-like problems (MVEPs) on Hadamard manifolds. Specifically, our aim is to establish error bounds for MVEPs. For this, we propose some regularized gap functions for MVEPs under suitable conditions. Then some error bounds for MVEPs in terms of regularized gap functions are obtained with the hypotheses imposed on the data of MVEPs. Our results in this paper are new and can be considered as a significant generalization of some previously known results in the literature.

Keywords:

• Mixed vector equilibrium-like problem
• gap function
• error bound
• Hadamard manifolds

2010 Mathematics Subject Classifications:

• 47J20
• 49J40

Acknowledgements

The authors are grateful to the editor and two anonymous referees for their valuable remarks which improved the results and presentation of this article.

Disclosure statement

No potential conflict of interest was reported by the author(s).