Linear Functional Analysis: Introduction to Lebesgue Integration and Infinite-Dimensional Problems.

1971 ◽  
Vol 78 (4) ◽  
pp. 417
Author(s):  
A. J. Silberger ◽  
Bernard Epstein
Keyword(s):  
Functional Analysis ◽  
Linear Functional ◽  
Infinite Dimensional ◽  
Lebesgue Integration

Controllability results of fractional integro-differential equation with non-instantaneous impulses on time scales

2020 ◽  
Author(s):  
Vipin Kumar ◽  
Muslim Malik
Keyword(s):  
Differential Equation ◽  
Functional Analysis ◽  
Time Scales ◽  
Linear Functional ◽  
Integro Differential Equation ◽  
Numerical Example ◽  
Contraction Theorem ◽  
Banach Contraction ◽  
Banach Contraction Theorem ◽  
Different Time Scales

Abstract In this work, we investigate the controllability results of a fractional integro-differential equation with non-instantaneous impulses on time scales. Banach contraction theorem and the non-linear functional analysis have been used to establish these results. In support, a numerical example with simulation for different time scales is given to validate the obtained analytical outcomes.

Linear Functional Analysis

10.1142/1557 ◽  
1992 ◽  
Author(s):  
Wladyslaw Orlicz ◽  
Lee Peng Yee
Keyword(s):  
Functional Analysis ◽  
Linear Functional

Topics in Non-Linear Functional Analysis

2002 ◽  
Vol 86 (505) ◽  
pp. 190
Author(s):  
Steve Abbott ◽  
Louis Nirenberg
Keyword(s):  
Functional Analysis ◽  
Linear Functional ◽  
Non Linear

scholarly journals Topological Quasilinear Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Yılmaz Yılmaz ◽  
Sümeyye Çakan ◽  
Şahika Aytekin
Keyword(s):  
Functional Analysis ◽  
Linear Functional ◽  
Vector Spaces ◽  
Multivalued Mappings ◽  
Linear Spaces ◽  
Localization Principle ◽  
Topological Vector Spaces

We introduce, in this work, the notion of topological quasilinear spaces as a generalization of the notion of normed quasilinear spaces defined by Aseev (1986). He introduced a kind of the concept of a quasilinear spaces both including a classical linear spaces and also nonlinear spaces of subsets and multivalued mappings. Further, Aseev presented some basic quasilinear counterpart of linear functional analysis by introducing the notions of norm and bounded quasilinear operators and functionals. Our investigations show that translation may destroy the property of being a neighborhood of a set in topological quasilinear spaces in contrast to the situation in topological vector spaces. Thus, we prove that any topological quasilinear space may not satisfy the localization principle of topological vector spaces.

Compactness of bounded trajectories of dynamical systems in infinite dimensional spaces

1979 ◽  
Vol 84 (1-2) ◽  
pp. 19-33 ◽  
Author(s):  
G. F. Webb
Keyword(s):  
Linear Functional ◽  
Infinite Dimensional ◽  
Volterra Integrodifferential Equation ◽  
Infinite Dimensional Banach Space ◽  
Age Dependent ◽  
Non Linear ◽  
Linear Functional Differential Equation ◽  
Functional Differential ◽  
Bounded Sets ◽  
Bounded Trajectories

SynopsisThe following theorem is proved: Let S(t), t≧0 be a dynamical system in an infinite dimensional Banach space X such that S(t) = S1(t)+S2(t) for t≧0, where (1) uniformly in bounded sets of x in X, and (2) S2(t) is compact for t sufficiently large. Then, if the orbit {S(t)x: t ≧0} of x ∈ X is bounded in X, it is precompact in X. Applications are made to an age dependent population model, a non-linear functional differential equation on an infinite interval, and a non-linear Volterra integrodifferential equation.

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