相关论文: On Some Characterizations of General s-Convex Func…
For a function defined on a convex set in a Euclidean space, midpoint convexity is the property requiring that the value of the function at the midpoint of any line segment is not greater than the average of its values at the endpoints of…
A generalised trapezoid inequality for convex functions and applications for quadrature rules are given. A refinement and a counterpart result for the Hermite-Hadamard inequalities are obtained and some inequalities for pdf's and…
The aim of this paper is to introduce and study the concept of a contra-semicontinuous function and further investigate the class of strongly $S$-closed spaces. We obtain some new decompositions of generalized continuous functions.
Convex analysis is fundamental to proving inequalities that have a wide variety of applications in economics and mathematics. In this paper we provide Jensen-type inequalities for functions that are, intuitively, "very" convex. These…
We study the convexity properties of the generalized trigonometric functions considered as functions of parameter. We show that $p\to\sin_p(y)$ and $p\to\cos_p(y)$ are log-concave on the appropriate intervals while $p\to\tan_p(y)$ is…
In this paper, the Authors establish a new identity for differentiable functions. By the well-known H\"older and power mean inequality, they obtain some integral inequalities related to the convex functions and apply these inequalities to…
In this paper, we introduce a new class of nonsmooth convex functions called SOS-convex semialgebraic functions extending the recently proposed notion of SOS-convex polynomials. This class of nonsmooth convex functions covers many common…
We introduce notions of concavity for functions on balanced polyhedral spaces, and we show that concave functions on such spaces satisfy several strong continuity properties.
In this paper we achieve some new Hadamard type inequalities using elementary well known inequalities for functions whose first derivatives absolute values are s-geometrically and geometrically convex. And also we get some applications for…
We analyze matrix convex functions of a fixed order defined on a real interval by differential methods as opposed to the characterization in terms of divided differences given by Kraus. We obtain for each order conditions for matrix…
The main aspect of this paper is to introduce a new generalisation of nano open sets namely, nano h-open sets. These newly generalised sets serve as the foundation for the definition of nano h-continuous functions and some results involving…
In this note we provide a full conjugacy and subdifferential calculus for convex convex-composite functions in finite-dimensional space. Our approach, based on infimal convolution and cone-convexity, is straightforward and yields the…
A general divergence measure for monotonic functions is introduced. Its connections with the f-divergence for convex functions are explored. The main properties are pointed out.
In this paper we give a characterization of all order isomorphisms on some classes of convex functions. We deal with the class $Cvx(K)$ consisting of lower-semi-continuous convex functions defined on a convex set $K$, and its subclass…
Generalized circumcenters have been recently introduced and employed to speed up classical projection-type methods for solving feasibility problems. In this note, circumcenters are enforced in a new setting; they are proven to provide…
This paper introduces a new subtraction operation for convex sets, which defines their difference as a collection of inclusion-minimal convex sets with appropriate definitions of linear operations on them. With these operations the set of…
We analyze a class of sublinear functionals which characterize the interior and the exterior of a convex cone in a normed linear space.
In this letter, we give a characterization for a generic construction of bent functions. This characterization enables us to obtain another efficient construction of bent functions and to give a positive answer on a problem of bent…
The paper is devoted to a comprehensive second-order study of a remarkable class of convex extended-real-valued functions that is highly important in many aspects of nonlinear and variational analysis, specifically those related to…
Extended real-valued functions are often used in optimization theory, but in different ways for infimum problems and for supremum problems. We present an approach to extended real-valued functions that works for all types of problems and…