A generalization of the strong Fitzpatrick inequality

Abstract

We present a generalization of the strong Fitzpatrick inequality in the context of reflexive Banach spaces, involving a twisted bigger conjugate function. We also introduce a related family of gap functions for maximal monotone inclusion problems.

Keywords:

• Strong Fitzpatrick inequality
• gap functions
• maximal monotone operators
• twisted bigger conjugate functions
• Tykhonov well-posed functions

Acknowledgements

We are very grateful to an anonymous referee, whose useful comments have helped us to improve the presentation. This author acknowledges financial support from the Spanish Ministry of Economy and Competitiveness, through Grant MTM2014-59179-C2-2-P and the Severo Ochoa Programme for Centres of Excellence in R&D (SEV-2015-0563), and under Australian Research Council’s Discovery Projects funding scheme (project number DP140103213).

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research was supported by CAPES [grant number BEX 3843/14-9]; the Spanish Ministry of Economy and Competitiveness [grant number MTM2014-59179-C2-2-P]; the Severo Ochoa Programme for Centres of Excellence in R&D [SEV-2015-0563]; Australian Research Council’s Discovery Projects funding scheme [project number DP140103213].