On stability analysis for generalized Minty variational-hemivariational inequality in reflexive Banach spaces

Lu-Chuan Ceng; Ravi P Agarwal; Jen-Chih Yao; Yonghong Yao

doi:10.1186/s13660-018-1890-9

On stability analysis for generalized Minty variational-hemivariational inequality in reflexive Banach spaces

J Inequal Appl. 2018;2018(1):298. doi: 10.1186/s13660-018-1890-9. Epub 2018 Oct 30.

Authors

Lu-Chuan Ceng¹, Ravi P Agarwal^{2

3}, Jen-Chih Yao⁴, Yonghong Yao⁵

Affiliations

¹ 1Department of Mathematics, Shanghai Normal University, Shanghai, China.
² 2Department of Mathematics, Texas A&M University, Kingsville, USA.
³ 3Florida Institute of Technology, Melbourne, USA.
⁴ 4Center for General Education, China Medical University, Taichung, Taiwan.
⁵ 5Department of Mathematics, Tianjin Polytechnic University, Tianjin, China.

Abstract

The stability for a class of generalized Minty variational-hemivariational inequalities has been considered in reflexive Banach spaces. We demonstrate the equivalent characterizations of the generalized Minty variational-hemivariational inequality. A stability result is presented for the generalized Minty variational-hemivariational inequality with $(f, J)$ -pseudomonotone mapping.

Keywords: Clarke’s generalized directional derivative; Generalized variational-hemivariational inequality; Pseudomonotone mapping; Reflexive Banach space; Stability.