Regularity of Refinable Functions Vectors.
Remark to a paper by J. A. Baker.
Remarks on recent fixed point theorems.
Remarks on strongly Wright-convex functions
Some properties of strongly Wright-convex functions are presented. In particular it is shown that a function f:D → ℝ, where D is an open convex subset of an inner product space X, is strongly Wright-convex with modulus c if and only if it can be represented in the form f(x) = g(x)+a(x)+c||x||², x ∈ D, where g:D → ℝ is a convex function and a:X → ℝ is an additive function. A characterization of inner product spaces by strongly Wright-convex functions is also given.
Remarks on the comparison of weighted quasi-arithmetic means
We present comparison theorems for the weighted quasi-arithmetic means and for weighted Bajraktarević means without supposing in advance that the weights are the same.
Representation formula for the entropy and functional inequalities
We prove a stochastic formula for the Gaussian relative entropy in the spirit of Borell’s formula for the Laplace transform. As an application, we give simple proofs of a number of functional inequalities.
Reverse functional inequalities and their applications to nonlinear elliptic boundary value problems.