It is shown that a locally Lipschitz function is approximately convex if, and only if, its Clarke subdifferential is a submonotone operator. Consequently, in finite dimensions, the class of locally Lipschitz approximately convex functions coincides with the class of lower-C functions. Directional approximate convexity is introduced and shown to be a natural extension of the class of lower-C fun...

This paper reviews the method of model-fitting via the empirical characteristic function. The advantage of using this procedure is that one can avoid difficulties inherent in calculating or maximizing the likelihood function. Thus it is a desirable estimation method when the maximum likelihood approach encounters difficulties but the characteristic function has a tractable expression. The basic...

We provide a Bayes-Nash equilibrium analysis of the simultaneous ascending auction (SAA) when local bidders interested in a single item compete against global bidders interested in aggregating many items. We first assume that each local bidder values only a specific item, e.g. the license for the region where it has monopoly power, and that global bidders’ valuation functions are convex. For th...

In this paper, a new type of convexity is defined, namely, the left–right-(k,h-m)-p IVM (set-valued function) convexity. Utilizing definition convexity, we prove Hadamard inequalities for noninteger Katugampola integrals. These generalize convex IVM, (p,h)-convex p-convex h-convex, s-convex in second sense and many other related well-known classes functions implicitly. An apt number numerical e...

Convexity and convex functions play an important role in theoretical physics. To initiate a study of the possible uses of convex functions in General Relativity, we discuss the consequences of a spacetime (M, gμν) or an initial data set (Σ, hij , Kij) admitting a suitably defined convex function. We show how the existence of a convex function on a spacetime places restrictions on the properties...

In this paper, we give a fundamental convexity preserving for spectral functions. Indeed, we investigate infimal convolution, Moreau envelope and proximal average for convex spectral functions, and show that this properties are inherited from the properties of its corresponding convex function. This results have many applications in Applied Mathematics such as semi-definite programmings and eng...

A jump system is defined as a set of integer points (vectors) with certain exchange property, generalizing the concepts matroids, delta-matroids, and base polyhedra integral polymatroids (or submodular systems). discrete convexity concept for functions on constant-parity systems it has been used in graph theory algebra. In this paper we call “jump M-convexity” extend to M♮-convexity” larger cla...

We study an interesting class of Banach function algebras of innitely dierentiable functions onperfect, compact plane sets. These algebras were introduced by Honary and Mahyar in 1999, calledLipschitz algebras of innitely dierentiable functions and denoted by Lip(X;M; ), where X is aperfect, compact plane set, M = fMng1n=0 is a sequence of positive numbers such that M0 = 1 and(m+n)!Mm+n ( m!Mm)...