scholarly journals Asymptotic properties of Banach spaces and coarse quotient maps

2018 ◽  
Vol 146 (11) ◽  
pp. 4723-4734
Author(s):  
Sheng Zhang
Keyword(s):  
Banach Spaces ◽  
Asymptotic Properties ◽  
Quotient Maps

scholarly journals ASYMPTOTIC PROPERTIES OF KOLMOGOROV WIDTHS

2010 ◽  
Vol 82 (1) ◽  
pp. 10-17
Author(s):  
MIKHAIL I. OSTROVSKII
Keyword(s):  
Banach Space ◽  
Asymptotic Behavior ◽  
Banach Spaces ◽  
Asymptotic Properties ◽  
Codimension One ◽  
Kolmogorov Widths

AbstractWe consider two problems concerning Kolmogorov widths of compacts in Banach spaces. The first problem is devoted to relations between the asymptotic behavior of the sequence of n-widths of a compact and of its projections onto a subspace of codimension one. The second problem is devoted to comparison of the sequence of n-widths of a compact in a Banach space 𝒴 and of the sequence of n-widths of the same compact in other Banach spaces containing 𝒴 as a subspace.

Weighted pseudo asymptotically Bloch periodic solutions to nonlocal Cauchy problems of integrodifferential equations in Banach spaces

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Yong-Kui Chang ◽  
Jianguo Zhao
Keyword(s):  
Banach Spaces ◽  
Mild Solutions ◽  
Asymptotic Properties ◽  
Auxiliary Result ◽  
Appreciable Effect ◽  
Cauchy Problems ◽  
State Variable ◽  
Strict Contraction ◽  
Forced Term ◽  
Nonlocal Cauchy Problem

Abstract This paper is mainly concerned with some new asymptotic properties on mild solutions to a nonlocal Cauchy problem of integrodifferential equation in Banach spaces. Under some well-imposed conditions on the nonlocal Cauchy, the neutral and forced terms, respectively, we establish some existence results for weighted pseudo S-asymptotically (ω, k)-Bloch periodic mild solutions to the referenced equation on R + ${\mathbb{R}}_{+}$ by suitable superposition theorems. The results show that the strict contraction of the nonlocal Cauchy and the neutral terms with the state variable has an appreciable effect on the existence and uniqueness of such a solution compared with the forced term. As an auxiliary result, the existence of weighted pseudo S-asymptotically (ω, k)-Bloch periodic mild solutions is deduced under the sublinear growth condition on the force term with its state variable. The existence of weighted pseudo S-asymptotically ω-antiperiodic mild solution is also obtained as a special example.

scholarly journals Asymptotic behavior of solutions to difference equations in Banach spaces

2021 ◽  
pp. 1-17
Author(s):  
Janusz Migda
Keyword(s):  
Asymptotic Behavior ◽  
Banach Spaces ◽  
Difference Equations ◽  
Asymptotic Properties ◽  
Sufficient Conditions ◽  
Degree Of Approximation ◽  
Asymptotic Behavior Of Solutions ◽  
Vector Version ◽  
A New Technique ◽  
Prescribed Asymptotic Behavior

We investigate the asymptotic properties of solutions to higher order nonlinear difference equations in Banach spaces. We introduce a new technique based on a vector version of discrete L'Hospital's rule, remainder operator, and the regional topology on the space of all sequences on a given Banach space. We establish sufficient conditions for the existence of solutions with prescribed asymptotic behavior. Moreover, we are dealing with the problem of approximation of solutions. Our technique allows us to control the degree of approximation of solutions.

scholarly journals Asymptotic geometry of Banach spaces and uniform quotient maps

2014 ◽  
Vol 142 (8) ◽  
pp. 2747-2762 ◽  
Author(s):  
S. J. Dilworth ◽  
Denka Kutzarova ◽  
G. Lancien ◽  
N. L. Randrianarivony
Keyword(s):  
Banach Spaces ◽  
Quotient Maps ◽  
Asymptotic Geometry

scholarly journals Functional differential equations with nonlocal initial conditions

1997 ◽  
Vol 10 (2) ◽  
pp. 145-156 ◽  
Author(s):  
Sergiu Aizicovici ◽  
Yun Gao
Keyword(s):  
Banach Spaces ◽  
Continuous Dependence ◽  
Evolution Equations ◽  
Initial Conditions ◽  
Asymptotic Properties ◽  
Functional Differential Equations ◽  
Cauchy Problems ◽  
Accretive Operators ◽  
Nonlocal Initial Conditions ◽  
Functional Differential

We study the existence, uniqueness, asymptotic properties, and continuous dependence upon data of solutions to a class of abstract nonlocal Cauchy problems. The approach we use is based on the theory of m-accretive operators and related evolution equations in Banach spaces.

Sign in / Sign up

Export Citation Format

Share Document