Related papers: Discontinuous Strongly Quasiconvex Functions

In this paper, we firstly prove the existence of the equilibrium for the generalized abstract economy. We apply these results to show the existence of solutions for systems of vector quasi-equilibrium problems with multivalued trifunctions.…

We discuss some surprising phenomena from basic calculus related to oscillating functions and to the theorem on the differentiability of inverse functions. Among other things, we see that a continuously differentiable function with a strict…

All continuous, SL$(n)$ and translation invariant valuations on the space of convex functions on ${\mathbb R}^n$ are completely classified.

In this paper, we derive new estimates for the remainder term of the midpoint, trapezoid, and Simpson formulae for functions whose derivatives in absolute value at certain power are quasi-convex. Some applications to special means of real…

Let $S$ be a seminorm on an infinite-dimensional real or complex vector space $X$. Our purpose in this note is to study the continuity and discontinuity properties of $S$ with respect to certain norm-topologies on $X$.

We study the class of compact convex subsets of a topological vector space which admits a strictly convex and lower semicontinuous function. We prove that such a compact set is embeddable in a strictly convex dual Banach space endowed with…

Functions that are piecewise defined are a common sight in mathematics while convexity is a property especially desired in optimization. Suppose now a piecewise-defined function is convex on each of its defining components - when can we…

It is well known that weakly continuous semigroups defined over $\mathbb{R}_{+}$ are automatically strongly continuous. We extend this result to more generally defined semigroups, including multiparameter semigroups.

In this paper, we have studied first the idea of rough continuity of real valued functions of real variables and then we have discussed some important properties of rough continuity. Then we study the idea of rough $I$-continuity of real…

Let $\Delta_m$ be the standard $m$-dimensional simplex of non-negative $m+1$ tuples that sum to unity and let $S$ be a nonempty subset of $\Delta_m$. A real valued function $h$ defined on a convex subset of a real vector space is $S$-almost…

This paper concerns three classes of real-valued functions on intervals, operator monotone functions, operator convex functions, and strongly operator convex functions. Strongly operator convex functions were previously treated in [3] and…

We investigate the differentiability properties of real-valued quasiconvex functions f defined on a separable Banach space X. Continuity is only assumed to hold at the points of a dense subset. If so, this subset is automatically residual.…

We study differentiable strongly quasiconvex functions for providing new properties for algorithmic and monotonicity purposes. Furthemore, we provide insights into the decreasing behaviour of strongly quasiconvex functions, applying this…

We prove some basic properties of quasinearly subharmonic functions and quasinearly subharmonic functions in the narrow sense.

We show that the non-centered maximal function of a BV function is quasicontinuous. We also show that \emph{if} the non-centered maximal functions of an SBV function is a BV function, then it is in fact a Sobolev function. Using a recent…

We classify all continuous valuations on the space of finite convex functions with values in the same space which are dually epi-translation-invariant and equi- resp. contravariant with respect to volume-preserving linear maps. We thereby…

In this paper we give various characterizations of quasiopen sets and quasicontinuous functions on metric spaces. For complete metric spaces equipped with a doubling measure supporting a p-Poincar\'e inequality we show that quasiopen and…

In this paper we give a description of separating or disjointness preserving linear bijections on spaces of vector-valued absolutely continuous functions defined on compact subsets of the real line. We obtain that they are continuous and…

A classification of upper semicontinuous, translation and dually epi-translation invariant valuations is established on the space of convex Lipschitz function on $\mathbb{R}$ with compact domain.

In this paper we show how the superquadratic functions can be used as a tool for researching other types of convex functions like $\phi $-convexity, strong-convexity and uniform convexity. We show how to use inequalities satisfied by…