We introduce a class of generalized relative entropies (inspired by the Bregman divergence in information theory) on the Wasserstein space over a weighted Riemannian or Finsler manifold. We prove that the convexity of all the entropies in this class is equivalent to the combination of the non-negative weighted Ricci curvature and the convexity of another weight function used in the definition o...

In this paper, the Schur convexity is generalized to Schur f -convexity, which contains the Schur geometrical convexity, harmonic convexity and so on. When f : R+ →R is defined by f (x) = (xm−1)/m if m = 0 and f (x) = lnx if m = 0 , the necessary and sufficient conditions for f -convexity (is called Schur m -power convexity) of Daróczy means are given, which improve, generalize and unify Shi et...

‎In the paper‎, ‎we study duality for vector equilibrium problems using a concept of generalized convexity in dealing with the quasi-relative interior‎. ‎Then‎, ‎their applications to optimality conditions for quasi-relative efficient solutions are obtained‎. ‎Our results are extensions of several existing ones in the literature when the ordering cones in both the objective space and the constr...

In the paper, the set-convexity and mapping-convexity properties of the extended images of generalized systems are considered. By using these image properties and the tools of topological linear spaces, separation schemes ensuring the impossibility of generalized systems are developed; then, special problem classes are investigated.

The usual duality results are established for mixed symmetric multiobjective dual programs without nonnegativity constraints using the notion of invexity/ generalized invexity which has allowed weakening various types of convexity/ generalized convexity assumptions. This mixed symmetric dual formulation unifies two existing symmetric dual formulations in the literature.