Remarks on t-quasiconvex functions
نویسندگان
چکیده
منابع مشابه
Hermite-Hadamard inequality for geometrically quasiconvex functions on co-ordinates
In this paper we introduce the concept of geometrically quasiconvex functions on the co-ordinates and establish some Hermite-Hadamard type integral inequalities for functions defined on rectangles in the plane. Some inequalities for product of two geometrically quasiconvex functions on the co-ordinates are considered.
متن کاملQuasiconvex functions and Hessian equations
In this note we construct new examples of quasiconvex functions defined on the set Sn×n of symmetric matrices. They are built on the k-th elementary symmetric function of the eigenvalues, k = 1, 2, ..., n. The idea is motivated by Šverák’s paper [S]. The proof of our result relies on the theory of the so-called k-Hessian equations, which have been intensively studied recently, see [CNS], [T], [...
متن کاملJensen’s Inequality for Quasiconvex Functions
This class of functions strictly contains the class of convex functions defined on a convex set in a real linear space. See [8] and citations therein for an overview of this issue. Some recent studies have shown that quasiconvex functions have quite close resemblances to convex functions – see, for example, [4], [6], [7], [10] for quasiconvex and even more general extensions of convex functions...
متن کاملQuasiconvex Functions and Nonlinear Pdes
A second order characterization of functions which have convex level sets (quasiconvex functions) results in the operator L0(Du,Du) = min{v ·D2u vT | |v| = 1, |v ·Du| = 0}. In two dimensions this is the mean curvature operator, and in any dimension L0(Du,Du)/|Du| is the first principal curvature of the surface S = u−1(c). Our main results include a comparison principle for L0(Du,Du) = g when g ...
متن کاملHadamard-type Inequalities for Quasiconvex Functions
Recently Hadamard-type inequalities for nonnegative, evenly quasiconvex functions which attain their minimum have been established. We show that these inequalities remain valid for the larger class containing all nonnegative quasiconvex functions, and show equality of the corresponding Hadamard constants in case of a symmetric domain.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematical Inequalities & Applications
سال: 2009
ISSN: 1331-4343
DOI: 10.7153/mia-12-54