We construct geodesics in the Wasserstein space of probability measures along which all the measures have an upper bound on their density that is determined by the densities of the endpoints of the geodesic. Using these geodesics we show that a local Poincaré inequality and the measure contraction property follow from the Ricci curvature bounds defined by Sturm. We also show for a large class o...

We introduce several types of the Levitin-Polyak well-posedness for a generalized vector quasivariational inequality problem with both abstract set constraints and functional constraints. Criteria and characterizations of these types of the Levitin-Polyak well-posednesses with or without gap functions of generalized vector quasivariational inequality problem are given. The results in this paper...

In the paper, we consider functional set-valued integral equations whose representation contains integrals occurring symmetrically on both sides of equation. On coefficients equation, impose certain conditions, more general than standard Lipschitz condition, which allow application Bihari–LaSalle inequality in proofs obtained theorems. this way, obtain a result about existence and uniqueness so...

We prove that synthetic lower Ricci bounds for metric measure spaces -- both in the sense of Bakry-\'Emery and Lott-Sturm-Villani can be characterized by various functional inequalities including local Poincar\'e inequalities, logarithmic Sobolev dimension independent Harnack inequality, inequality. More generally, these equivalences will proven setting time-dependent provide a characterization...