Fenchel Conjugates on the Product of a Hadamard Manifold and Its Tangent Bundle
Applicable Nonlinear Analysis, Volume 3, Issue 3, December 2026, Pages: 233–242
Aida Jahangir
Department of Mathematics, Faculty of Sciences, Golestan University, Gorgan, Golestan, Iran
Mehdi Roohi
Department of Mathematics, Faculty of Sciences, Golestan University, Gorgan, Golestan, Iran
Abstract
The interplay between convexity and duality is fundamental in optimization theory. Extending these ideas from Euclidean spaces to Riemannian manifolds, particularly Hadamard manifolds, has attracted significant attention due to applications in nonlinear geometric structures. In this paper, we study the theory of Fenchel conjugation and its generalizations on Hadamard manifolds for functions defined on the product of a manifold and its tangent bundle. We introduce the concepts of parametric conjugate, biconjugate, and establish their fundamental properties, including order-preserving behavior, translation invariance and scaling properties. These results extend basic properties of convex analysis to the manifold setting. The results obtained in this paper can be applied in duality theory and optimization on Hadamard manifolds.
Cite this Article as
Aida Jahangir and Mehdi Roohi, Fenchel Conjugates on the Product of a Hadamard Manifold and Its Tangent Bundle, Applicable Nonlinear Analysis, 3(3), 233–242, 2026