Recently, the higher order averaging method for studying periodic solutions of both Lipschitz differential equations and discontinuous piecewise smooth was developed in terms Brouwer degree theory. Between equations, there is a huge class lacking analysis on existence solutions, namely continuous non-Lipschitz equations. In this paper, based coincidence theory nonlinear operator we perform (non...

Let X, Y be complete metric spaces and E, F be Banach spaces. A bijective linear operator from a space of E-valued functions on X to a space of F -valued functions on Y is said to be biseparating if f and g are disjoint if and only if Tf and Tg are disjoint. We introduce the class of generalized Lipschitz spaces, which includes as special cases the classes of Lipschitz, little Lipschitz and uni...

This is a survey article. We consider different problems in connection with the behavior of functions of operators under perturbations of operators. We deal with three classes of operators: unitary operators, self-adjoint operators, and contractions. We study operator Lipschitz and operator differentiable functions. We also study the behavior of functions under perturbations of an operator by a...

We show that the Scott topology induces a topology for real-valued Lipschitz maps on Banach spaces which we call the L-topology. It is the weakest topology with respect to which the L-derivative operator, as a second order functional on the space of Lipschitz maps into the domain of non-empty, convex and weak*-compact valued functions ordered by reverse inclusion, is continuous. For finite dime...

In this papermodular convergence theorems inOrlicz spaces for multivariate extensions of the one-dimensional moment operator are given and the order of modular convergence in modular Lipschitz classes is studied.

Let R 2 be a bounded domain with Lipschitz boundary and let : ! R be a function which is measurable and bounded away from zero and innnity. We consider the divergence form elliptic operator

The continuity for some multilinear operators generated by certain integral operators and Lipschitz functions on some Hardy and Herz-type spaces are obtained. The operators include Littlewood-Paley operators, Marcinkiewicz operators and Bochner-Riesz operator.

Some Lipschitz norm and BMO norm inequalities for potential operator to the versions of differential forms are obtained, and some properties of a new kind of A λ3 r λ 1 , λ 2 , ΩΩ weight are derived.

We characterize compact composition operators on real Banach spaces of complex-valued bounded Lipschitz functions on metric spaces, not necessarily compact, with Lipschitz involutions and determine their spectra.