相关论文: Convexity and sandwich theorems

We present the construction of a theory of distributions (generalized functions) with a ``thick submanifold'', that is, a new theory of thick distributions on $\mathbb{R}^n$ whose domain contains a smooth submanifold on which the test…

We study the topology of complete Finsler manifolds admitting convex functions

We analyze a class of sublinear functionals which characterize the interior and the exterior of a convex cone in a normed linear space.

We discuss some aspects of the theory of subelliptic estimates.

In this paper, the author introduces the concept of the symmetrized p-convex function, gives Hermite-Hadamard type inequalities for symmetrized p-convex functions.

In this paper we established new integral inequalities which are more general results for coordinated convex functions on the coordinates by using some classical inequalities.

We show a new, elementary and geometric proof of the classical Alexandrov theorem about the second order differentiability of convex functions. We also show new proofs of recent results about Lusin approximation of convex functions and…

Tensor fields depending on other tensor fields are considered. The concept of extended tensor fields is introduced and the theory of differentiation for such fields is developed.

We study a special class of non-convex functions which appear in nonlinear elasticity; and we prove that they have well-defined Legandre transforms. Several examples are given, and an application to a nonlinear eigenvalue problem

This is an overview of merging the techniques of Riesz space theory and convex geometry.

We give a closed formula for the Conway function of a splice in terms of the Conway function of its splice components. As corollaries, we refine and generalize results of Seifert, Torres, and Sumners-Woods.

We prove an infinite $(p,q)$-theorem for piercing fat compact convex sets in $\RR^d$ with $k$-flats. Additionally, we develop a new framework through which infinite $(p,q)$-theorems concerning compact sets and $k$-flats can be extended to…

We establish an edge of the wedge theorem for the sheaf of holomorphic functions with exponential growth at infinity and construct the sheaf of Laplace hyperfunctions in several variables. We also study the fundamental properties of the…

In this short note we present several infinite dimensional theorems which generalize corresponding facts from the finite dimensional differential inclusions theory.

In this article, we obtain two interesting general inequalities concerning Riemman sums of convex functions, which in particular, sharpen Alzer's inequality and give a suitable converse for it.

The existence of a homogeneous decomposition for continuous and epi-translation invariant valuations on super-coercive functions is established. Continuous and epi-translation invariant valuations that are epi-homogeneous of degree $n$ are…

In this paper, we initiate the study of the geometric function theory for slice starlike functions over quaternions and its subclasses. This allows us to answer negatively some questions about the Bieberbach conjecture, the growth,…

A class of real functions, which is the generalization of a family of convex functions, is introduced; in this connection, we have defined $X$-convex, strictly $X$-convex, quasi-$X$-convex, strictly quasi-$X$-convex, and semi-strictly…

For a convex domain $D$ that is enclosed by the hypersurface $\partial D$ of bounded normal curvature, we prove an angle comparison theorem for angles between $\partial D$ and geodesic rays starting from some fixed point in $D$, and the…

In this paper, we establish some integral ineuqalities for n- times differentiable convex functions.