On the continuity of midpoint hall convex set-valued functions.
On the continuity of midpoint hull convex set-valued functions. (Summary).
On the convexity of high order of sequences.
On the equality condition in Hölder's and Minkowski inequalities.
On the equality condition in Hölder's and Minkowski's inequalities. (Summary).
On the functional equation f(...(x) + g(y)) = ..(x) * h(x+y). (Short Communication).
On the functional equation f(...(x) + g(y)) = ...(x) * h(x+y).
On the generalizations of two Ozeki's results
On the identric and logarithmic means.
On the impossibility of approximating convex functions with ones.
On the lower hull of convex functions.
On the Moser-Onofri and Prékopa-Leindler inequalities.
Using elementary convexity arguments involving the Legendre transformation and the Prékopa-Leindler inequality, we prove the sharp Moser-Onofri inequality, which says that1/16π ∫|∇φ|2 + 1/4π ∫ φ - log (1/4π ∫ eφ) ≥ 0for any funcion φ ∈ C∞(S2).
On the reduction of pairs of bounded closed convex sets
Let X be a Hausdorff topological vector space. For nonempty bounded closed convex sets A,B,C,D ⊂ X we denote by A ∔ B the closure of the algebraic sum A + B, and call the pairs (A,B) and (C,D) equivalent if A ∔ D = B ∔ C. We prove two main theorems on reduction of equivalent pairs. The first theorem implies that, in a finite-dimensional space, a pair of nonempty compact convex sets with a piecewise smooth boundary and parallel tangent spaces at some boundary points is not minimal. The second theorem...
On the speed of convergence of iteration of a function.
On the strengthened Jordan's inequality.
On the Subdifferential of the Supremum of Two Convex Functions.
On the support of midconvex operators.
On the support of midconvex operators. (Summary).
On ω-convex functions
In Orlicz spaces theory some strengthened version of the Jensen inequality is often used to obtain nice geometrical properties of the Orlicz space generated by the Orlicz function satisfying this inequality. Continuous functions satisfying the classical Jensen inequality are just convex which means that such functions may be described geometrically in the following way: a segment joining every pair of points of the graph lies above the graph of such a function. In the current paper we try to obtain...
Ostrowski, Grüss, Čebyšev type inequalities for functions whose second derivatives belong to and whose modulus of second derivatives are convex.