Search results for "Picard–Lindelöf theorem"

Generalized Weyl's theorem and quasi-affinity

2010

An Integral Version of Ćirić’s Fixed Point Theorem

2011

We establish a new fixed point theorem for mappings satisfying a general contractive condition of integral type. The presented theorem generalizes the well known Ciric's fixed point theorem [Lj. B. Ciric, Generalized contractions and fixed point theorems, Publ. Inst. Math. 12 (26) (1971) 19-26]. Some examples and applications are given.

Schaefer–Krasnoselskii fixed point theorems using a usual measure of weak noncompactness

2012

Abstract We present some extension of a well-known fixed point theorem due to Burton and Kirk [T.A. Burton, C. Kirk, A fixed point theorem of Krasnoselskii–Schaefer type, Math. Nachr. 189 (1998) 423–431] for the sum of two nonlinear operators one of them compact and the other one a strict contraction. The novelty of our results is that the involved operators need not to be weakly continuous. Finally, an example is given to illustrate our results.

Some characterizations of operators satisfying a-Browder's theorem

2005

Abstract We characterize the bounded linear operators T defined on Banach spaces satisfying a-Browder's theorem, or a-Weyl's theorem, by means of the discontinuity of some maps defined on certain subsets of C . Several other characterizations are given in terms of localized SVEP, as well as by means of the quasi-nilpotent part, the hyper-kernel or the analytic core of λ I − T .

Variations on Weyl's theorem

2006

AbstractIn this note we study the property (w), a variant of Weyl's theorem introduced by Rakočević, by means of the localized single-valued extension property (SVEP). We establish for a bounded linear operator defined on a Banach space several sufficient and necessary conditions for which property (w) holds. We also relate this property with Weyl's theorem and with another variant of it, a-Weyl's theorem. We show that Weyl's theorem, a-Weyl's theorem and property (w) for T (respectively T*) coincide whenever T* (respectively T) satisfies SVEP. As a consequence of these results, we obtain that several classes of commonly considered operators have property (w).

Analytic solutions of the Navier-Stokes equations

2001

We consider the time dependent incompressible Navier-Stokes equations on an half plane. For analytic initial data, existence and uniqueness of the solution are proved using the Abstract Cauchy-Kovalevskaya Theorem in Banach spaces. The time interval of existence is proved to be independent of the viscosity.

Radó–Kneser–Choquet theorem

2014

We present a new approach to the celebrated theorem of Rado–Kneser–Choquet (RKC) on univalence of planar harmonic mappings. The novelty lies in establishing a continuous path (isotopy) from the given harmonic map to a conformal one. Along this path the mappings retain positive Jacobian determinant by virtue of so-called Minimum Principle. These ideas extend to nonlinear uncoupled systems of partial differential equations, as in Iwaniec, Koski and Onninen [‘Isotropic p-harmonic systems in 2D, Jacobian estimates and univalent solutions’, Rev. Mat. Iberoam, to appear]. Unfortunately, details of such digression would lead us too far afield. Nonetheless, one gains (in particular) the RKC-Theorem…

The Third Main Theorem

1998

The Second Main Theorem

1998

THE BISHOP-PHELPS-BOLLOBAS THEOREM FOR BILINEAR FORMS

2013

In this paper we provide versions of the Bishop-Phelps-Bollobás Theorem for bilinear forms. Indeed we prove the first positive result of this kind by assuming uniform convexity on the Banach spaces. A characterization of the Banach space Y Y satisfying a version of the Bishop-Phelps-Bollobás Theorem for bilinear forms on ℓ 1 × Y \ell _1 \times Y is also obtained. As a consequence of this characterization, we obtain positive results for finite-dimensional normed spaces, uniformly smooth spaces, the space C ( K ) \mathcal {C}(K) of continuous functions on a compact Hausdorff topological space K K and the space K ( H ) K(H) of compact operators on a Hilbert space H H . On the other hand, the B…