Fan’s minimax inequality is extended to the context of metric spaces with global nonpositive curvature. As a consequence, a much more general result on the existence of a Nash equilibrium is… (More)

Given a function f : I → J and a pair of means M and N, on the intervals I and J respectively, we say that f is MN -convex provided that f (M(x, y)) N(f (x), f (y)) for every x , y ∈ I . In this… (More)

We present new short proofs for both Stirlings formula and Stirlings formula for the Gamma function. Our approach in the rst case relies upon analysis of Wallisformula, while the second result… (More)

T. Popoviciu [7] has proved in 1965 an interesting characterization of the convex functions of one real variable, relating the arithmetic mean of its values and the values taken at the barycenters of… (More)

equality holds in either side only for the affine functions (i.e., for the functions of the form mx + n). The middle point (a + b)/2 represents the barycenter of the probability measure 1 b−adx… (More)

One proves that the Mazur-Ulam theorem can be extended in the framework of metric spaces as long as a well behaved concept of midpoint is available. This leads to the new concept of Mazur-Ulam space.… (More)

Constantin P. Niculescu and Ionel Rovenţa Department of Mathematics, University of Craiova, 200585 Craiova, Romania Correspondence should be addressed to Ionel Rovenţa, roventaionel@yahoo.com… (More)