– We present a one-dimensional version of the functional form of the geometric Brunn-Minkowski inequality in free (noncommutative) probability theory. The proof relies on matrix approximation as used recently by P. Biane and F. Hiai, D. Petz and Y. Ueda to establish free analogues of the logarithmic Sobolev and transportation cost inequalities for strictly convex potentials, that are recovered ...

and Applied Analysis 3 Note that the inequality (14) holds true with constantC = √ 2 if T ≥ 1/2 (see [9]). Subsequently, we may assume this condition is fulfilled. Consider a functional I : E T → R defined by

In this article, we prove a local Sobolev inequality for complete Ricci flows. Our main result is that the ν-functional of disk on flow depends only Nash entropy based at center disk, and consequently volume disk. Furthermore, introduce some applications inequality. These reveal way in which geometry evolves along flow. particular, show several classical theorems related to Perelman's monotonic...

In this paper, we establish a functional generalization of Minkowski’s type inequality on time scales based on diamond-α integral, which is introduced as a linear combination of the delta and nabla integrals. Some related results are also obtained.

We establish a relation between the Schwarz inequality and the generalized concurrence of an arbitrary, pure, bipartite or tripartite state. This relation places concurrence in a geometrical and functional-analytical setting.

In this paper, we investigate homomorphisms from unital C∗−algebras to unital Banach algebras and derivations from unital C∗−algebras to Banach A−modules related to a Cauchy–Jensen functional inequality. Mathematics subject classification (2010): 39B72, 46H30, 46B06.

We use a coupling method for functional stochastic differential equations with bounded memory to establish an analogue of Wang’s dimension-free Harnack inequality [13]. The strong Feller property for the corresponding segment process is also obtained.

The Francfort–Marigo model of brittle fracture is posed in terms of the minimization of a highly irregular energy functional. A successful method for discretizing the model is to work with an approximation of the energy. In this work a generalised Ambrosio–Tortorelli functional is used. This leads to a bound-constrained minimization problem, which can be posed in terms of a variational inequali...

We prove that a function of several variables satisfying a functional differential inequality with unbounded delay can be estimated by a solution of a suitable initial problem for an ordinary functional differential equation. As a consequence of the comparison theorem we obtain a Perrontype uniqueness result and a result on continuous dependence of solutions on given functions for partial funct...