Search

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]

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 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]

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]

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]