Search

In the paper it is considered a convex programming problem (CPP) with functional and non-functional constraints. In contrast to previous works, in the study of convex optimization problems, we do not deal with the classical approach of perturbations. In particular, thanks to the new representation of the indicator function on a convex set, the successful use of the infimal convolution method in this work plays a key role in proving duality results for problem CPP. Also, we consider a convex mathematical programming problem with inequality and linear equality constraints given by some matrix. In this case, it turns out that the dual cone to the cone of tangent directions coincides with the set of the image of the points of transposed matrix, taken with a minus sign. [ABSTRACT FROM AUTHOR]

In this paper we establish some quasilinearity properties of some functionals associated to a weakened Davis-Choi-Jensen's inequality for positive maps and convex (concave) functions. Applications for power function are also provided. [ABSTRACT FROM AUTHOR]

The paper deals with the optimal control problem described by second-order differential inclusions. Based on the infimal convolution concept of convex functions, dual problems for differential inclusions are constructed and the results of duality are proved. In this case, it turns out that Euler-Lagrange type inclusions are \duality relations" for both primary and dual problems. In particular, the linear second-order optimal control problem with the Mayer functional is considered. This problem shows that maximization in the dual problems is realized over the set of solutions of the adjoint equation. Finally, we construct the dual problem to the problem with the second-order polyhedral differential inclusion. [ABSTRACT FROM AUTHOR]

In this paper, some approximation properties of (p, q)-analogue of Bernstein-Stancu operators are studied. Rate of statistical convergence by means of modulus of continuity and Lipschitz type maximal functions has been investigated. Monotonicity of (p, q)-Bernstein-Stancu operators and a global approximation theorem by means of Ditzian-Totik modulus of smoothness is established. A quantitative Voronovskaja type theorem is developed for these operators. Furthermore, we show comparisons and some illustrative graphics for the convergence of operators to a function. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and study some new classes of convex functions which are called generalized harmonic convex and generalized harmonic log-convex functions. These new classes of harmonic functions unify serval new and previous known classes of harmonic convex functions. We derive some estimates for the class of functions whose certain powers of the absolute value are generalized harmonic convex function. Results obtained in this paper continue to hold for several classes of harmonic convex functions, which can be viewed as special cases. The ideas and techniques of this may inspire research in this field. [ABSTRACT FROM AUTHOR]

Making use of the Hadamard product (or convolution), we find some estimates for symmetric points, related to shell-like curves connected with Fibonacci numbers. We determine the initial Taylor-Maclaurin coefficients | a2 | and | a3 | for functions belonging to the class of Bi-univalent functions of the Bazilevic type of order γ. We also obtain the Fekete-Szego result for the function class. [ABSTRACT FROM AUTHOR]

In this paper, we obtain Gauss type inequalities for the class of convex functions. Further, we give an application of new inequalities to obtain Stolarsky type means. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce some characterizations of (Gaussian) hypergeometric function to be in various subclasses of uniformly starlike and uniformly convex functions. Operators related to hypergeometric functions are also considered. Some of our results correct previously known results. [ABSTRACT FROM AUTHOR]

The theory of m-convex (m-cv) functions is a new direction in the theory of real geometry. However, for m = 1 this class coincides with the class of convex functions, and for m = n it coincides with the class of subharmonic functions, which, as is known, have been well studied (A.Aleksandrov, I.Bakelman, A.Pogorelov, N.Ivochkina, I.Privalov, etc.) The definition of m - cv functions for 1 < m < n has a very different nature, which uses high-order Hessians. Functions for such m have been considered in a series of works by N. Trudinger, X. Wang and others. In this article, we establish a connection between m-convex functions and strongly m-subharmonic (shm) functions and, using the well-known properties of shm functions, we prove a number of important properties of the class of m - cv functions. [ABSTRACT FROM AUTHOR]