相关论文: Global mixed \L ojasiewicz inequalities and asympt…

In this paper, we give some {\L}ojasiewicz-type inequalities and a nonsmooth slope inequality on non-compact domains for continuous definable functions in an o-minimal structure. We also give a necessary and sufficicent condition for which…

The classical Lojasiewicz inequality and its extensions for partial differential equation problems (Simon) and to o-minimal structures (Kurdyka) have a considerable impact on the analysis of gradient-like methods and related problems:…

We consider \L ojasiewicz inequalities for a non-degenerate holomorphic function with an isolated singularity at the origin. We give an explicit estimation of the \L ojasiewicz exponent in a slightly weaker form than the assertion in…

We generalize the well-known mean value inequality of subharmonic functions for a slightly more general function class. We also apply this generalized mean value inequality to weighted boundary behavior and nonintegrability questions of…

We present a global version of the {\L}ojasiewicz inequality on comparing the rate of growth of two polynomial functions in the case the mapping defined by these functions is (Newton) non-degenerate at infinity. In addition, we show that…

This paper is devoted to proving the general {\L}ojasiewicz inequality, in both the definable and subanalytic cases, under the most relaxed assumptions. It means that we drop the usual continuity and compactness assumptions. In the second…

We give a strong version of a classic inequality of \L ojasiewicz; one which collapses to the usual inequality in the complex analytic case. We show that this inequality for a pair, quadruple, or octuple of real analytic functions allows us…

We give an effective estimation from above for the local {\L}ojasiewicz exponent for separation of semialgebraic sets and for a semialgebraic mapping on a closed semialgebraic set. We also give an effective estimation from below of the…

The Lojasiewicz inequalities for real analytic functions on Euclidean space were first proved by Stanislaw Lojasiewicz (1965) using methods of semianalytic and subanalytic sets, arguments later simplified by Bierstone and Milman (1988). In…

The ostrowski inequality expresses bounds on the deviation of a function from its integral mean. The aim of this paper is to establish a new inequality using weight function which generalizes the inequalities of Dragomir, Wang and Cerone…

We consider the exponent of \L ojasiewicz inequality $\|\partial\,f(\mathbf z)\| \ge c |f(\mathbf z|^\theta$ for two classes of analytic functions and we will give an explicit estimation for $\theta$. First we consider certain…

A celebrated result of Hal\'asz describes the asymptotic behavior of the arithmetic mean of an arbitrary multiplicative function with values on the unit disc. We extend this result to multilinear averages of multiplicative functions…

The main goal of this paper is to present some explicit formulas for computing the {{\L}}ojasiewicz exponent in the {{\L}}ojasiewicz inequality comparing the rate of growth of two real bivariate analytic function germs.

In this paper we prove existence and multiplicity results of unbounded critical points for a general class of weakly lower semicontinuous functionals. We will apply a suitable nonsmooth critical point theory.

We demonstrate that the failure of $L^1$ regularity in Calder\'on-Zygmund theory is a universal phenomenon: every non-constant holomorphic function in $\C^n$ generates a counterexample to the Poisson equation. In order to achieve this goal,…

We establish the existence and nonexistence of entire solutions to a semilinear elliptic problem whose nonlinearity is the critical power multiplied by a function that takes the value 1 in an open bounded region and the value -1 in its…

Generalizations of Ostrowski type inequality for functions of Lipschitzian type are established. Applications in numerical integration and cumulative distribution functions are also given.

In this paper we prove a gap phenomenon for critical points of the $H$-functional on closed non-spherical surfaces when $H$ is constant, and in this setting furthermore prove that sequences of almost critical points satisfy {\L}ojasiewicz…

This paper is devoted to present new error bounds of regularized gap functions for polynomial variational inequalities with exponents explicitly determined by the dimension of the underlying space and the number/degree of the involved…

Let $f: (\mathbb{C}^n,0) \rightarrow (\mathbb{C},0)$ be a semiquasihomogeneous function. We give a formula for the local {\L}ojasiewicz exponent $\mathcal{L}_{0}(f)$ of $f$, in terms of weights of $f$. In particular, in the case of a…