The book contains invited papers by well-known experts on a wide range of topics (economics, variational analysis, probability etc.) closely related to convexity and generalized convexity, and refereed contributions of specialists from the world on current research on generalized convexity and...

1 Theory of point-set maps -- 1.1 Introductory concepts -- 1.2 Superlinear functionals and convex sets -- 1.3 Elements of the topological theory of point-set maps -- 1.4 Superlinear maps and their duals -- 2 The Neumann-Gale model -- 2.1 Formulation of the Neumann-Gale model -- 2.2 Rates of...

We study increasing quasiconcave functions which are co-radiant. Such functions have frequently been employed in microeconomic analysis. The study is carried out in the contemporary framework of abstract convexity and abstract concavity. Various properties of these functions are derived. In...

We study increasing quasiconcave functions which are co-radiant. Such functions have frequently been employed in microeconomic analysis. The study is carried out in the contemporary framework of abstract convexity and abstract concavity. Various properties of these functions are derived. In...

Generalizations of the classical concept of a convex function have been proposed in various fields such as economics, management science, engineering, statistics and applied sciences during the second half of this century. In addition to new results in more established areas of generalized...

Various generalizations of convex functions have been introduced in areas such as mathematical programming, economics, management science, engineering, stochastics and applied sciences, for example. Such functions preserve one or more properties of convex functions and give rise to models which...