Known Results and Open Problems on C1 linearization in Banach Spaces
نویسندگان
چکیده
The purpose of this paper is to review the results obtained by the authors on linearization of dynamical systems in infinite dimensional Banach spaces, especially in the C case, and also to present some open problems that we believe that are still important for the understanding of the theory. The purpose of the present paper is to make a review of results obtained by the authors in the field of linearization of dynamical systems in infinite dimensional Banach spaces, with a focuss on C1 linearization of contractions, with the intention of stating in the right context a number of open problems we believe it would be worth to be solved. 1991Mathematics Subject Classification. AMS Classification. Primary: 37C15, 35B05 Secondary: 34C20, 37D05.
منابع مشابه
On some open problems in cone metric space over Banach algebra
In this paper we prove an analogue of Banach and Kannan fixed point theorems by generalizing the Lipschitz constat $k$, in generalized Lipschitz mapping on cone metric space over Banach algebra, which are answers for the open problems proposed by Sastry et al, [K. P. R. Sastry, G. A. Naidu, T. Bakeshie, Fixed point theorems in cone metric spaces with Banach algebra cones, Int. J. of Math. Sci. ...
متن کاملLinearization of class C for contractions on Banach Spaces
In this work we prove a C1-linearization result for contraction diffeomorphisms, near a fixed point, valid in infinite dimensional Banach spaces. As an intermediate step, we prove a specific result of existence of invariant manifolds, which can be interesting by itself and that was needed on the proof of our main theorem. Our results essentially generalize some classical results by P. Hartman i...
متن کاملSufficient Enlargements in the Study of Projections in Normed Linear Spaces
The study of sufficient enlargements of unit balls of Banach spaces forms a natural line of attack of some well-known open problems of Banach space theory. The purpose of the paper is to present known results on sufficient enlargements and to state some open problems.
متن کاملMangasarian-Fromovitz and Zangwill Conditions For Non-Smooth Infinite Optimization problems in Banach Spaces
In this paper we study optimization problems with infinite many inequality constraints on a Banach space where the objective function and the binding constraints are Lipschitz near the optimal solution. Necessary optimality conditions and constraint qualifications in terms of Michel-Penot subdifferential are given.
متن کاملNew hybrid method for equilibrium problems and relatively nonexpansive mappings in Banach spaces
In this paper, applying hybrid projection method, a new modified Ishikawa iteration scheme is presented for finding a common element of the solution set of an equilibrium problem and the set of fixed points of relatively nonexpansive mappings in Banach spaces. A numerical example is given and the numerical behaviour of the sequences generated by this algorithm is compared with several existence...
متن کامل