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Journals and Conferences
In this paper we prove that the Newton method applied to the generalized equation y ∈ f(x) + F (x) with a C function f and a set-valued map F acting in Banach spaces, is locally convergent uniformly… (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 norm–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 there… (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 rotund… (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. Preliminaries… (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 δX(ε) cε2, is found. The estimate… (More)
We consider renormings in function spaces which are uniformly convex in every direction, uniformly Gâteaux smooth or have some related properties.
We present equivalent conditions for a space X with an unconditional basis to admit an equivalent norm with a strictly convex dual norm.