The Brøndsted-Rockafellar theorem in geodesic spaces

Key Points

• The aim is to present a constructive version of the Brøndsted-Rockafellar theorem applicable in general geodesic metric spaces.
• Developed a constructive formulation of the Brøndsted-Rockafellar theorem within geodesic metric spaces.
• Explored applications involving Caristi’s fixed point theorem and quantitative relationships.
• Analyzed metric slope error bounds related to the global growth of functionals.
• Proposed a new constructive form of Caristi’s fixed point theorem applicable to geodesic spaces.
• Established quantitative relationships between metric slope error bounds and functional growth.