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Finitary/static semantics in the form of intersection type assignments have become a paradigm for analysing the fine structure of all sorts of lambda-models. The key step is the construction of a filter model isomorphic to a given…

Perhaps, it is not too far from the truth to say that, among the great concepts (as compactness, completeness, order, convexity) on which functional analysis is based, connectedness is relatively less popular, though this does not mean that…

Functions with uniform sublevel sets can represent orders, preference relations or other binary relations and thus turn out to be a tool for scalarization that can be used in multicriteria optimization, decision theory, mathematical…

Discrete analogs of the index transforms, involving Bessel and the modified Bessel functions are introduced and investigated. The corresponding inversion theorems for suitable classes of functions and sequences are established.

Extending the investigations about the theory of duals, we analyze duals built up with the aid of discrete symmetry operators. We scrutinize algebraic and physical constraints (encompassing them in a theoretical scope) in order to verify…

This paper is devoted to the study of generalized differentiation properties of the infimal convolution. This class of functions covers a large spectrum of nonsmooth functions well known in the literature. The subdifferential formulas…

In this paper, we introduce new properties of the relative interior calculus for nearly convex sets, functions, and set-valued mappings. These properties are important for the development of duality theory in optimization. Then we…

In this paper we give a review of the method of imsets introduced by Studeny (2005) from a geometric point of view. Elementary imsets span a polyhedral cone and its dual cone is the cone of supermodular functions. We review basic facts on…

In the last several years, the intimate connection between convex optimization and learning problems, in both statistical and sequential frameworks, has shifted the focus of algorithmic machine learning to examine this interplay. In…

Finding the minimum and the minimizers of convex functions has been of primary concern in convex analysis since its conception. It is well-known that if a convex function has a minimum, then that minimum is global. The minimizers, however,…

Some concepts, such as non-compactness measure and condensing operators, defined on metric spaces are extended to uniform spaces. Such extensions allow us to locate, in the context of uniform spaces, some classical results existing in…

We focus on three different convexity principles for local and nonlocal variational integrals. We prove various generalizations of them, as well as their equivalences. Some applications to nonlinear eigenvalue problems and Hardy-type…

In this paper, we establish some new integral inequalities for $(\alpha, m)-$convex functions and quasi-convex functions, respectively. Our results in special cases recapture known results.

We consider discrete metric spaces and we look for non-constant contractions. We introduce the notion of contractive map and we characterize the spaces with non-constant contractive maps. We provide some examples to discussion the possible…

Murota et al. have recently developed a theory of discrete convex analysis which concerns M-convex functions on jump systems. We introduce here a family of M-concave functions arising naturally from polynomials (over a field of generalized…

It is known that several discrete integrals, including the Choquet and Sugeno integrals as well as some of their generalizations, are comonotonically modular functions. Based on a recent description of the class of comonotonically modular…

We explore the applications of Lorentzian polynomials to the fields of algebraic geometry, analytic geometry and convex geometry. In particular, we establish a series of intersection theoretic inequalities, which we call rKT property, with…

In this paper, we introduce a subclass of close-to-convex functions defined in the open unit disk. We obtain the inclusion relationships, coefficient estimates and Fekete-Szego inequality. The results presented here would provide extension…

Fracture functions, originally suggested to describe the production of diffractive and leading hadrons in semi-inclusive DIS, may be also applied at fixed target energies. They may also include interference and final state interaction,…

WDC sets in ${\mathbb R}^d$ were recently defined as sublevel sets of DC functions (differences of convex functions) at weakly regular values. They form a natural and substantial generalization of sets with positive reach and still admit…