In this paper we prove that the Newton method applied to the generalized equation y âˆˆ f(x) + F (x) with a C function f and a set-valued map F acting in Banach spaces, is locally convergent uniformlyâ€¦ (More)

Some new classes of compacta K are considered for which C(K) endowed with the pointwise topology has a countable cover by sets of small local normâ€“diameter.

It is shown that an Orlicz sequence space hM admits an equivalent analytic renorming if and only if it is either isomorphic to l2n or isomorphically polyhedral. As a consequence, we show that thereâ€¦ (More)

We consider two classes of nonlinear maps between normed spaces which are relevant for the study of Banach spaces that admit equivalent locally uniformly rotund and midpoint locally uniformly rotundâ€¦ (More)

We prove that in quadratic perturbations of generic Hamiltonian vector fields with two saddle points and one center there can appear at most two limit cycles. This bound is exact. 1. Preliminariesâ€¦ (More)

An upper bound q(c) for the best, under equivalent renorming, possible power type of the modulus of smoothness of a Banach space with modulus of convexity satisfying Î´X(Îµ) cÎµ2, is found. The estimateâ€¦ (More)