We generalize the well-known Hölder inequality and give a condition at which the equality holds.

We give a Jensen’s operator inequality for strongly convex functions. As a corollary, we improve Hölder-McCarthy inequality under suitable conditions. More precisely we show that if Sp (A) ⊂ I ⊆ (1,∞), then 〈Ax, x〉 r ≤ 〈Ax, x〉 − r − r 2 (

Abstract. We prove an inequality for Hölder continuous differential forms on compact manifolds in which the integral of the form over the boundary of a sufficiently small, smoothly immersed disk is bounded by a certain multiplicative convex combination of the volume of the disk and the area of its boundary. This inequality has natural applications in dynamical systems, where Hölder forms are ub...

Keywords: m-convex functions Hermite–Hadamard inequalities Hölder inequality Power-mean inequality a b s t r a c t In this paper we give some estimates to the right-hand side of Hermite–Hadamard inequality for functions whose absolute values of second derivatives raised to positive real powers are m-convex.

* Correspondence: [email protected]. cn Department of Mathematics, Harbin Institute of Technology, Harbin 150001, PR China Abstract In this paper, we obtain the weak reverse Hölder inequality of weakly A-harmonic sensors and establish the Hölder continuity of A-harmonic sensors. Mathematics Subject Classification 2010: 58A10 · 35J60

We introduce and study the k-cap condition and use it to prove that the quasiconformal image of a Hölder domain is itself Hölder if and only if it supports a Trudinger inequality. We compare and contrast the k-cap condition with related slice-type conditions.

In this talk we deal with a more precise estimates for the matrix versions of Young, Heinz, and Hölder inequalities. First we give an improvement of the matrix Heinz inequality for the case of the Hilbert-Schmidt norm. Then, we refine matrix Young-type inequalities for the case of Hilbert-Schmidt norm, which hold under certain assumptions on positive semidefinite matrices appearing therein. Fin...