Related papers: An operational test for existence of a consistent …
The notion of ordinal concavity of utility functions has recently been considered by Hafalir, Kojima, Yenmez, and Yokote in economics while there exist earlier related works in discrete optimization and operations research. In the present…
This work is concerned with the existence and uniqueness of boundary value problems defined on semi-infinite intervals. These kinds of problems seldom admit exactly known solutions and, therefore, the theoretical information on their…
Sufficient conditions are identified under which the value function and the optimal strategy of a Markov decision process (MDP) are even and quasi-convex in the state. The key idea behind these conditions is the following. First, sufficient…
This paper is devoted to the study of approximate solutions for a multiobjective interval-valued optimization problem based on an interval order. We establish new existence theorems of approximate solutions for such a problem under some…
This research aimed to introduce the concept of harmonically m-concave set-valued functions, which is obtained from the combination of two definitions: harmonically m-concave functions and set-valued functions. In this work some properties…
The notion of a real-valued function is central to mathematics, computer science, and many other scientific fields. Despite this importance, there are hardly any positive results on decision procedures for predicate logical theories that…
When uncertainty is modelled by a set of non-dominated and non-compact probability measures, a notion of essential supremum for a family of real-valued functions is developed in terms of upper semi-analytic functions. We show how the…
Consider a real-valued function that can only be observed with stochastic noise at a finite set of design points within a Euclidean space. We wish to determine whether there exists a convex function that goes through the true function…
In this paper, we investigate and find a necessary and sufficient condition for a function to be absolutely continuous over $\mathbb{R}$ (denoted by $AC(\mathbb{R})$) or any unbounded interval in $\mathbb{R}$ . Note that the Lebesgue's…
A function $F$ defined on all subsets of a finite ground set $E$ is quasi-concave if $F(X\cup Y)\geq\min\{F(X),F(Y)\}$ for all $X,Y\subset E$. Quasi-concave functions arise in many fields of mathematics and computer science such as social…
Eliciting a preference model involves asking a person, named decision-maker, a series of questions. We assume that these preferences can be represented by an additive value function. In this work, we query simultaneously two decision-makers…
A formal likelihood ratio hypothesis test for the validity of a parametric regression function is proposed, using a large-dimensional, nonparametric double cone alternative. For example, the test against a constant function uses the…
While periodic responses of periodically forced dissipative nonlinear mechanical systems are commonly observed in experiments and numerics, their existence can rarely be concluded in rigorous mathematical terms. This lack of a priori…
This work focuses on the mathematical study of constant function market makers. We rigorously establish the conditions for optimal trading under the assumption of a quasilinear, but not necessarily convex (or concave), trade function. This…
A class of real functions, which is the generalization of a family of convex functions, is introduced; in this connection, we have defined $X$-convex, strictly $X$-convex, quasi-$X$-convex, strictly quasi-$X$-convex, and semi-strictly…
This paper provides an unique dual representation of set-valued lower semi-continuous quasiconvex and convex functions. The results are based on a duality result for increasing set valued functions.
In partial function extension, we are given a partial function consisting of $n$ points from a domain and a function value at each point. Our objective is to determine if this partial function can be extended to a function defined on the…
In this paper we give some sufficient conditions of analyticity and univalence for functions defined by an integral operator. Next, we refine the result to a quasiconformal extension criterion with the help of the Becker's method. Further,…
We prove that every nonnegative continuous real-valued function on a given compact metric space is the uniform limit of some increasing sequence of nonnegative simple functions being linear combinations of indicators of open sets; here the…
Necessary and sufficient conditions for convexity and strong convexity, respectively, of sublevel sets that are defined by finitely many real-valued $C^{1,1}$-maps are presented. A novel characterization of strongly convex sets in terms of…