In this work we deal with the so-called path convexities, defined over special collections of paths. For example, the collection of the shortest paths in a graph is associated with the well-known geodesic convexity, while the collection of the induced paths is associated with the monophonic convexity ; and there are many other examples. Besides reviewing the path convexities in the literature, ...

We study the existence of Stackelberg equilibrium points on strategy sets which are geodesic convex in certain Riemannian manifolds by using metric projection arguments. The present results extend those obtained in Nagy [J. Global Optimization (2013)] in the Euclidean context.

The Bregman divergence (Bregman distance, Bregman measure of distance) is a certain useful substitute for a distance, obtained from a well-chosen function (the “Bregman function”). Bregman functions and divergences have been extensively investigated during the last decades and have found applications in optimization, operations research, information theory, nonlinear analysis, machine learning ...

We prove the existence of a contraction rate for Vlasov-Fokker-Planck equation in Wasserstein distance, provided interaction potential is Lipschitz continuous and confining both (locally) greater than quadratic function, thus requiring no convexity conditions. Our strategy relies on coupling methods suggested by A. Eberle [22] adapted to kinetic setting enabling also obtain uniform time propaga...

Abstract We identify a norm-dense subspace of the dual sequence space $$l^{(p,\infty )}$$ l ( p , ∞ ) , thus closing existing gap in literature. based our approach on notion James...

Let X be a Banach space with closed unit ball B. Given k ∈ N, X is said to be k-β, repectively, (k + 1)-nearly uniformly convex ((k + 1)-NUC), if for every ε > 0, there exists δ, 0 < δ < 1, so that for every x ∈ B, and every ε-separated sequence (xn) ⊆ B, there are indices (ni) k i=1, respectively, (ni) k+1 i=1 , such that 1 k+1 ‖x + ∑k i=1 xni‖ ≤ 1 − δ, respectively, 1 k+1 ‖ ∑k+1 i=1 xni‖ ≤ 1−...

There exists a surface of a convex polyhedron P and a partition L of P into geodesic convex polygons such that there are no connected"edge"unfoldings of P without self-intersections (whose spanning tree is a subset of the edge skeleton of L).

It is shown that a subset of a uniformly convex normed space is nearly convex if and only if its closure is convex. Also, a normed space satisfying a mild completeness property is strictly convex if and only if every metrically convex subset is convex. 1 Classical and constructive mathematics The arguments in this paper conform to constructive mathematics in the sense of Errett Bishop. This mea...