Convexity is a simple and natural notion which can be traced back to Archimedes (circa 250
BC), in connection with his famous estimate of the value of π (by using inscribed and …

Approach your problems from the right end It isn't! hat they can't see the solution. It is and
begin with the answers. Then one day, that they can't see the problem. perhaps you will find …

This book takes a comprehensive look at mean value theorems and their connection with
functional equations. Besides the traditional Lagrange and Cauchy mean value theorems, it …

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)) 6 N (f (x), f (y)) for every x, y 2 I. In this …

We investigate the correspondence between operator monotone functions and Stieltjes
functions. Then we shall prove that the class of nonnegative operator monotone functions is …

We raise several elementary questions pertaining to various aspects of means. These
questions refer to both known and newly introduced families of means, and include …

Abstract k-Adic formulations (for groups of objects of size k) of a variety of 2-adic similarity
coefficients (for pairs of objects) for binary (presence/absence) data are presented. The …

The perspective function is useful in convex analysis. In the study of operator theory, an
operator mean can be realized as the operator perspective and its limits. On the other hand …

For positive scalars a and b the contraharmonic mean of a and b, C(a,b), is defined by
C(a,b)=(a^2+b^2)/(a+b). In this paper we consider a natural matrix generalization of the …

The mean value theorem of integral calculus states that for any continuous realvalued
function f on an interval I, and for any two distinct real numbers a, b∈ I, there exists a value V …