Lipschitz class

Purpose: Study the existence of inertial manifolds and the asymptotic behavior of solutions to certain classes of evolution equations in an infinite-dimensional Banach space. The evolution equations considered with the linear parts is the generator of a semigroup and the Lipschitz coefficient of the nonlinear term may depend on time and belongs to admissible function spaces which contain wide classes of function spaces like Lp-spaces, the Lorentz spaces Lp,q and many other function spaces occurring in interpolation theory.

27p tunelove 10-06-2021 21 3   Download

One of effective approaches to the study of long - time behavior of infinite dimensional dynamical systems is based on the concept of inertial manifolds which was introduced by C. Foias, G. Sell and R. Temam (see [4] and the references therein). These inertial manifolds are finite dimensional Lipschitz ones, attract trajectories at exponential rate. This enables us to reduce the study of infinite dimensional systems to a class of induced finite dimensional ordinary differential equations.

14p trinhthamhodang1218 18-03-2021 14 2   Download

In the present work we prove some direct and inverse theorems for approximation by trigonometric polynomials in Musielak–Orlicz spaces. Furthermore, we get a constructive characterization of the Lipschitz classes in these spaces.

20p nutifooddau 21-01-2019 14 2   Download

The concern of this paper is to obtain the rate of convergence in terms of the partial and complete modulus of continuity and the degree of approximation by means of Lipschitz-type class for the bivariate operators.

18p danhdanh27 07-01-2019 26 1   Download

A class of multiobjective fractional programming problems (MFP) is considered where the involved functions are locally Lipschitz. In order to deduce our main results, we introduce the definition of (p,r) − ρ − (η,θ) - invex class about the Clarke generalized gradient. Under the above invexity assumption, sufficient conditions for optimality are given. Finally, three types of dual problems corresponding to (MFP) are formulated, and appropriate dual theorems are proved.

20p vinguyentuongdanh 19-12-2018 26 1   Download

In this paper, we define some new generalizations of strongly convex functions of order m for locally Lipschitz functions using Clarke subdifferential. Suitable examples illustrating the non emptiness of the newly defined classes of functions and their relationships with classical notions of pseudoconvexity and quasiconvexity are provided.

16p danhnguyentuongvi27 19-12-2018 37 1   Download

A well-known open question is whether every countable collection of Lipschitz functions on a Banach space X with separable dual has a common point of Fr´chet differentiability. We show that the answer is positive for e some infinite-dimensional X. Previously, even for collections consisting of two functions this has been known for finite-dimensional X only (although for one function the answer is known to be affirmative in full generality).

33p tuanloccuoi 04-01-2013 48 5   Download