Lipschitz r-continuity of the approximative subdifferential of a convex function.
Logarithmische Konvexität und Ungleichungsscharen.
Martin's axiom and medial functions.
Mean value theorem for convex functionals
Metrically convex functions in normed spaces
Properties of metrically convex functions in normed spaces (of any dimension) are considered. The main result, Theorem 4.2, gives necessary and sufficient conditions for a function to be metrically convex, expressed in terms of the classical convexity theory.
Midpoint convex functions majorized by midpoint concave functions.
Midpoint convex functions majorized by midpoint concave functions. (Short Communication).
Modified log-Sobolev inequalities for convex functions on the real line. Sufficient conditions
We provide a mild sufficient condition for a probability measure on the real line to satisfy a modified log-Sobolev inequality for convex functions, interpolating between the classical log-Sobolev inequality and a Bobkov-Ledoux type inequality. As a consequence we obtain dimension-free two-level concentration results for convex functions of independent random variables with sufficiently regular tail decay. We also provide a link between modified log-Sobolev inequalities...
Moments of Convex and Monotone Functions.
Monotone and convex -algebra valued functions.
Morse-Sard theorem for delta-convex curves
Let be a delta-convex mapping, where is an open interval and a Banach space. Let be the set of critical points of . We prove that has zero -dimensional Hausdorff measure.
Multiplicative concavity of the integral of multiplicatively concave functions.
n-Convex Functions in Linear Spaces.
Necessary and sufficient conditions for generalized convexity
We give some necessary and sufficient conditions for an n-1 times differentiable function to be a generalized convex function with respect to an unrestricted n-parameter family.
Necessary and sufficient conditions for Schur geometrical convexity of the four-parameter homogeneous means.
Nonlinear contractive conditions: A comparison and related problems
We establish five theorems giving lists of nonlinear contractive conditions which turn out to be mutually equivalent. We derive them from some general lemmas concerning subsets of the plane which may be applied both in the single- or set-valued case as well as for a family of mappings. A separation theorem for concave functions is proved as an auxiliary result. Also, we discuss briefly the following problems for several classes of contractions: stability of procedure of successive approximations,...
Note on some Hadamard-type inequalities.
Notes on some inequalities for convex functions
Notes on some inequalities for convex sequences and for k-convex functions