Jensen's inequality for quasiconvex functions
نویسندگان
چکیده
منابع مشابه
Jensen’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 کاملHermite-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 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 کاملJENSEN’S INEQUALITY FOR GG-CONVEX FUNCTIONS
In this paper, we obtain Jensen’s inequality for GG-convex functions. Also, we get in- equalities alike to Hermite-Hadamard inequality for GG-convex functions. Some examples are given.
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 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: Numerical Algebra, Control and Optimization
سال: 2012
ISSN: 2155-3289
DOI: 10.3934/naco.2012.2.279