Banach spaces

Purpose: Study the existence of inertial manifolds and the asymptotic behavior of solutions to certain classes of evolution equations in an infinite-dimensional Banach space. The evolution equations considered with the linear parts is the generator of a semigroup and the Lipschitz coefficient of the nonlinear term may depend on time and belongs to admissible function spaces which contain wide classes of function spaces like Lp-spaces, the Lorentz spaces Lp,q and many other function spaces occurring in interpolation theory.

27p tunelove 10-06-2021 22 3   Download

It is the objective of this paper to prove some xed point theorems for multivalued mappings. Among other things, we extend Theorem 1.3 to nonself-mappings. Also a simple proof of Theorem 1.3 is presented. Moreover, we give an armative answer to a question of Deimling. A negative answer to a question of Downing and Kirk is included as well.

14p larachdumlanat127 20-12-2020 7 2   Download

In this paper, on the base of the discrepancy principle for regularization parameter choice, the convergence rates of the regularized solution as well as its Galerkin approximations for nonlinear ill-posed problems with m-accretive perturbations are established without demanding the weak continuity of the duality mapping of the Banach spaces.

8p tamynhan5 10-12-2020 8 2   Download

Research optimality conditions for local weak efficient solution in vector equilibrium problem involving set, inequality and equality constraints with stable functions via contingent derivatives in finite-dimensional spaces. Research optimality conditions for weak, Henig, global and superefficient solutions in vector equilibrium problems with steady. Research second order optimality conditions for weak, Henig, global, super-efficient solutions in vector equilibrium problems with arbitrary functions in terms of contingent epiderivatives in Banach spaces.

26p xacxuoc4321 11-07-2019 17 5   Download

The results of this thesis are: Propose and prove the strong convergence of a new modification of the Newton-Kantorovich iterative regularization method (0.6) to solve the problem (0.1) with A is a monotone mapping from Banach space E into the dual space E ∗ , which overcomes the drawbacks of method (0.6).

26p xacxuoc4321 09-07-2019 25 5   Download

Bài viết trình bày điều kiện ổn định mũ của các hệ phương trình sai phân phụ thuộc thời gian có chậm, với biến liên tục, hệ phương trình sai phân ngẫu nhiên trong không gian Banach. Để nắm nội dung mời các bạn cùng tham khảo.

10p danhnguyentuongvi 17-12-2018 36 1   Download

In this paper, we establish the condition for convergence of X∞ m=1 X∞ n=1 1 mn E  kSmnk (mn) 1/p q for double arrays of independent random elements in Banach spaces following the type proposed by Li, Qi and Rosalsky.

12p tonymina21 05-12-2018 18 1   Download

The aim of this paper is to study convergence rates of the regularized solutions in connection with the finite-dimensional approximations for the operator equation of Hammerstein type x+ F2F1(x)=f in reflexive Banach spaces under the perturbations for not only the operators Fi,i=1,2, but also f.

9p binhminhmuatrenngondoithonggio 09-06-2017 29 2   Download

Đề tài không đi sâu vào nghiên cứu ứng dụng của các định lý điểm bất động mà chỉ trình bày khái niệm nón, một số tính chất cơ bản của nón trong không gian Banach, khái niệm không gian metric nón, cuối cùng là trình bày và chứng minh lại các định lý điểm bất động đã có trong bài báo: “Cone metric spaces and fixed point theorems of contractive mappings” của L.-G. Huang và X. Zhang một cách chi tiết và có hệ thống.

26p bautroibinhyen24 20-04-2017 60 3   Download

We introduce the notion of cotype of a metric space, and prove that for Banach spaces it coincides with the classical notion of Rademacher cotype. This yields a concrete version of Ribe’s theorem, settling a long standing open problem in the nonlinear theory of Banach spaces. We apply our results to several problems in metric geometry. Namely, we use metric cotype in the study of uniform and coarse embeddings, settling in particular the problem of classifying when Lp coarsely or uniformly embeds into Lq . We also prove a nonlinear analog of the Maurey-Pisier theorem, and use it to...

53p dontetvui 17-01-2013 65 8   Download

Introduction and statement of results Let E ⊂ Rn , and m ≥ 1. We write C m (E) for the Banach space of all real-valued functions ϕ on E such that ϕ = F on E for some F ∈ C m (Rn ). The natural norm on C m (E) is given by ϕ C m (E) = inf{ F C m (Rn ) : F ∈ C m (Rn ) and F = ϕ on E} . Here, as usual, C m (Rn ) is the space of real-valued functions on Rn with continuous and bounded derivatives through order m; and F C m (Rn ) = |β|≤m x∈Rn max sup |∂ β F (x)| .

58p noel_noel 17-01-2013 52 6   Download

The main question studied in this article may be viewed as a nonlinear analogue of Dvoretzky’s theorem in Banach space theory or as part of Ramsey theory in combinatorics. Given a finite metric space on n points, we seek its subspace of largest cardinality which can be embedded with a given distortion in Hilbert space. We provide nearly tight upper and lower bounds on the cardinality of this subspace in terms of n and the desired distortion. Our main theorem states that for any 0, every n point metric space contains a subset of size at least n1−...

68p noel_noel 17-01-2013 36 5   Download

Dedicated to the memory of V. I. Gurarii Abstract We prove that if X is a separable infinite dimensional Banach space then its isomorphism class has infinite diameter with respect to the Banach-Mazur distance. One step in the proof is to show that if X is elastic then X contains an isomorph of c0 .

16p noel_noel 17-01-2013 47 4   Download

A well-known open question is whether every countable collection of Lipschitz functions on a Banach space X with separable dual has a common point of Fr´chet differentiability. We show that the answer is positive for e some infinite-dimensional X. Previously, even for collections consisting of two functions this has been known for finite-dimensional X only (although for one function the answer is known to be affirmative in full generality).

33p tuanloccuoi 04-01-2013 49 5   Download

MAXIMAL REGULAR BOUNDARY VALUE PROBLEMS IN BANACH-VALUED WEIGHTED SPACE RAVI P. AGARWAL, MARTIN BOHNER, AND VELI B. SHAKHMUROV Received 10 July 2004 This study focuses on nonlocal boundary value problems for elliptic ordinary and partial differential-operator equations of arbitrary order, defined in Banach-valued function spaces. The region considered here has a varying bound and depends on a certain parameter.

34p sting12 10-03-2012 36 4   Download

NONSMOOTH AND NONLOCAL DIFFERENTIAL EQUATIONS IN LATTICE-ORDERED BANACH SPACES ¨ SIEGFRIED CARL AND S. HEIKKILA Received 7 September 2004 We derive existence results for initial and boundary value problems in lattice-ordered Banach spaces. The considered problems can be singular, functional, discontinuous, and nonlocal. Concrete examples are also solved. 1. Introduction In this paper, we apply fixed point results for mappings in partially ordered function spaces to derive existence results for initial and boundary value problems in an ordered Banach space E.

15p sting12 10-03-2012 29 3   Download

HYERS-ULAM STABILITY OF THE LINEAR RECURRENCE WITH CONSTANT COEFFICIENTS DORIAN POPA Received 5 November 2004 and in revised form 14 March 2005 Let X be a Banach space over the field R or C, a1 ,...,a p ∈ C, and (bn )n≥0 a sequence in X. We investigate the Hyers-Ulam stability of the linear recurrence xn+p = a1 xn+p−1 + · · · + a p−1 xn+1 + a p xn + bn , n ≥ 0, where x0 ,x1 ,...,x p−1 ∈ X. 1. Introduction In 1940, S. M. Ulam proposed the following problem. Problem 1.1. Given a metric group (G,...

7p sting12 10-03-2012 26 3   Download

PERIODIC SOLUTIONS FOR A COUPLED PAIR OF DELAY DIFFERENCE EQUATIONS GUANG ZHANG, SHUGUI KANG, AND SUI SUN CHENG Received 31 January 2005 and in revised form 24 March 2005 Based on the fixed-point index theory for a Banach space, positive periodic solutions are found for a system of delay difference equations. By using such results, the existence of nontrivial periodic solutions for delay difference equations with positive and negative terms is also considered. 1.

12p sting12 10-03-2012 39 5   Download

MANN ITERATION CONVERGES FASTER THAN ISHIKAWA ITERATION FOR THE CLASS OF ZAMFIRESCU OPERATORS G. V. R. BABU AND K. N. V. V. VARA PRASAD Received 3 February 2005; Revised 31 March 2005; Accepted 19 April 2005 The purpose of this paper is to show that the Mann iteration converges faster than the Ishikawa iteration for the class of Zamfirescu operators of an arbitrary closed convex subset of a Banach space. Copyright © 2006 Hindawi Publishing Corporation. All rights reserved. 1. Introduction Let E be a normed linear space, T : E → E a given operator. Let x0 ∈ E be arbitrary...

6p sting12 10-03-2012 39 5   Download

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: APPROXIMATING ZERO POINTS OF ACCRETIVE OPERATORS WITH COMPACT DOMAINS IN GENERAL BANACH SPACES HIROMICHI MIYAKE AND WATARU TAKAHASHI

10p sting11 10-03-2012 41 3   Download