On quadratic stochastic processes.
On convex stochastic processes.
Report of Meeting: The Thiertieth International Symposium on Functional Equations, September 20 - 26, 1992, Oberwolfach, Germany.
On midpoint convex set-valued functions.
On quadratic stochastic processes (Short Communication).
Midpoint convex functions majorized by midpoint concave functions.
Midpoint convex functions majorized by midpoint concave functions. (Short Communication).
On the support of midconvex operators.
On the support of midconvex operators. (Summary).
On convex stochastic processes (Short Communication).
On some class of midconvex functions
On -invariant measures and a functional equation
A characterization of midconvex set-valued functions
A sandwich theorem and Hyers-Ulam stability of affine functions.
A selection theorem of Helly type and its applications
We prove an abstract selection theorem for set-valued mappings with compact convex values in a normed space. Some special cases of this result as well as its applications to separation theory and Hyers-Ulam stability of affine functions are also given.
Minkowski sums of Cantor-type sets
The classical Steinhaus theorem on the Minkowski sum of the Cantor set is generalized to a large class of fractals determined by Hutchinson-type operators. Numerous examples illustrating the results obtained and an application to t-convex functions are presented.
Abstract separation theorems of Rodé type and their applications
Sufficient and necessary conditions are presented under which two given functions can be separated by a function Π-affine in Rodé sense (resp. Π-convex, Π-concave). As special cases several old and new separation theorems are obtained.
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.
Continuity properties of convex-type set-valued maps.
Characterizations of inner product spaces by strongly convex functions.
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