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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.
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].