Abstract Convexity, Some Relations and Applications

Applications of convexity in some identification problems

The Sharpening of Some Inequalities via Abstract Convexity

One of the application areas of abstract convexity is inequality theory. In this work, the authors seek to derive new inequalities by sharpening well-known inequalities by the use of abstract convexity. Cauchy-Schwarz inequality, Minkowski inequality and well-known mean inequalities are studied in this sense, concrete results are obtained for some of them. Mathematics subject classification (20...

Abstract Convexity and Augmented Lagrangians

Convexity and Augmented Lagrangians Regina S. Burachik University of South Australia and University of Ballarat Workshop on Advances in Continuous Optimization Reykjavik, Iceland Friday June 30 and Saturday July 1, 2006

Some Results on Convexity and Concavity of Multivariate Copulas

This paper provides some results on different types of convexity and concavity in the class of multivariate copulas. We also study their properties and provide several examples to illustrate our results.

Symmetrization, convexity and applications

Based on permutation enumeration of the symmetric group and ‘generalized’ barycentric coordinates on arbitrary convex polytope, we develop a technique to obtain symmetrization procedures for functions that provide a unified framework to derive new Hermite-Hadamard type inequalities. We also present applications of our results to the Wright-convex functions with special emphasis on their key rol...