There exist several characterizations of concavity for univariate functions. One of them states that a function is concave if and only if it has nonincreasing differences. This definition provides a natural generalization of concavity for multivariate functions called inframodularity. Inframodular transfers are defined and it is shown that a finite lottery is preferred to another by all expecte...

Moreover, if p , q, then the inequality is strict. A proof: The map u 7→ −u log u is strictly concave on [0, 1]; this follows from the fact that its derivative −(1 + log u) is strictly decreasing on [0, 1]. Now, a sum of concave functions is concave, so we conclude that H is concave. Moreover, if p , q, then they differ in some coordinate; strict concavity of the map u 7→ −u log u applied to th...

The Arrow-Pratt (A-P) definitions of absolute and relative risk aversion dominate the discussion of risk aversion and defining “more risk averse”. Ross (Econometrica 49:621–663, 1981) notes, however, that being A-P more risk averse is not sufficient for addressing many important comparative static questions. Consequently he introduces “a new and stronger measure for comparing two agents’ attitu...

In this paper, we study sufficient conditions for existence and uniqueness of solutions of three point boundary vale problem for p-Laplacian fractional order differential equations. We use Schauder's fixed point theorem for existence of solutions and concavity of the operator for uniqueness of solution. We include some examples to show the applicability of our results.

In this paper, we prove that the linear transformation yi = i ∑ j=0 ( m+ i n+ j ) xj , i = 0, 1, 2, . . . preserves the log-concavity property. © 2002 Elsevier Science Inc. All rights reserved.

We propose an approach to the attractors of skew products that tries to avoid unnecessary structures on the base space and rejects the assumption on the invariance of an attractor. When nonivertible maps in the base are allowed, one can encounter the mystery of the vanishing attractor. In the second part of the paper, we show that if the fiber maps are concave interval maps then contraction in ...

We observe that for any logarithmically concave nite sequence a 0 , a 1 , : : : , a n of positive integers there is a representation of the Lie algebra sl 2 (C) from which this logarithmic concav-ity follows. Thus, in applying this strategy to prove logarithmic concavity, the only issue is to construct such a representation naturally from given combinatorial data. As an example, we do this when...