Remarks on strongly convex functions

Some properties of strongly convex functions are presented. A characterization of pairs of functions that can be separated by a strongly convex function and a Hyers?CUlam stability result for strongly convex functions are given. An integral Jensen-type inequality and a Hermite?CHadamard-type inequality for strongly convex functions are obtained. Finally, a relationship between strong convexity and generalized convexity in the sense of Beckenbach is shown.     

Invariant pseudometrics on Palais proper G-spaces

Let G be a locally compact Hausdorff group. It is proved that: 1. on each Palais proper G-space X there exists a compatible family of G-invariant pseudometrics; 2.the existence of a compatible G-invariant metric on a metrizable proper G-space X is equivalent to the paracompactness of the orbit space X/G; 3. if in addition G is either almost connected or separable, and X is locally separable, then there exists a compatible G-invariant metric on X. This revised version was published online in June 2006 with corrections to the Cover Date.     

Remarks on convex functions and separable sequences

In this paper we extend some recent results on convex functions due to Dragomir [Some majorisation type discrete inequalities for convex functions, Math. Inequal. Appl. 7 (2) (2004) 207–216].     

Comparison of the Kobayashi-Royden and Sibony metrics on ring domains

In this paper we show that the Kobayashi-Royden metric and the Sibony metric are different on ring domains, i.e., the difference of two concentric balls, in higher dimension.     

Remarks on some completely monotonic functions

Applying the Euler-Maclaurin summation formula, we obtain upper and lower polynomial bounds for the function , x>0, with coefficients the Bernoulli numbers Bk. This enables us to give simpler proofs of some results of H. Alzer and F. Qi et al., concerning complete monotonicity of certain functions involving the gamma function Γ(x), the psi function ψ(x) and the polygamma functions ψ(n)(x), n=1,2,… .     

Remarks on the perturbation of analytic matrix functions

Integral Equations and Operator Theory -     

Remarks on the reflection principle for harmonic functions

The author was partially supported by the National Science Foundation under grant DMS-8618755.     

Remarks on subharmonic functions on riemannian manifolds

Sunto Si prova un teorema di limitatezza per funzioni subarmoniche su una varietà riemanniana completa M e soddisfacenti la condisione (A) (cfr. anche [8])e se ne danno alcune applicazioni allo studio del volume di M, dello spazio delle forme armoniche a coefficienti in fibrati vettoriali su M, di cette mappe armoniche definite su M.     

Remarks on Lempert functions of balanced domains

This note should clarify how the behavior of certain invariant objects reflects the geometric convexity of balanced domains. Authors’ addresses: Nikolai Nikolov, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev 8, 1113 Sofia, Bulgaria; Peter Pflug, Carl von Ossietzky Universit?t Oldenburg, Institut für Mathematik, Fakult?t V, Postfach 2503, D-26111 Oldenburg, Germany     

关于单叶函数中几个结果的注记

首先就Mbius变换在几何函数论上应用时存在的两个误区予以讨论,指出其存在的问题与如何改正;其次明确地指出用Baernstein方法估计m次对称单叶函数之逆函数系数时的不足之处;最后就S ingh与Puri一文中的一个结果给以改正,并用Ruschew eyh的共轭方法得到该结果成立的最佳范围.     

Remarks on Lempert functions of balanced domains

This note should clarify how the behavior of certain invariant objects reflects the geometric convexity of balanced domains.     

Remarks on the perturbation of analytic matrix functions III

As in [N], [LN] the Newton diagram is used in order to get information about the first terms of the Puiseux expansions of the eigenvalues () of the perturbed matrix pencilT(, )=A()+B(, ) in the neighbourhood of an unperturbed eigenvalue () ofA(). In fact sufficient conditions are given which assure that the orders of these first terms correspond to the partial multiplicities of the eigenvalue ₀ ofA().     

Remarks on g-functions on H^n

In this paper, the authors study some properties of Littlewood-Paley g-functions gψ（f）,Lusin area functions Sψ,α（f） and Littlewood-Paley gψ^＊,λ（f） functions defined on H^n, where α,λ 〉 0 and ψ, f are suitable functions. They are the generalization of the corresponding operators on R^n.