Linear Functional Analysis

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.

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Topics in Non-Linear Functional Analysis

The Mathematical Gazette ◽

10.2307/3621643 ◽

2002 ◽

Vol 86 (505) ◽

pp. 190

Author(s):

Steve Abbott ◽

Louis Nirenberg

Keyword(s):

Functional Analysis ◽

Linear Functional ◽

Non Linear

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Appendix A Introduction to Linear Functional Analysis

Mathematical Physics - North-Holland Mathematics Studies ◽

10.1016/s0304-0208(08)73796-4 ◽

1988 ◽

pp. 311-327

Keyword(s):

Functional Analysis ◽

Linear Functional

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Aspects of p-Adic Non-Linear Functional Analysis

10.1063/1.2193126 ◽

2006 ◽

Author(s):

Helge Glöckner

Keyword(s):

Functional Analysis ◽

Linear Functional ◽

Non Linear

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Topological Quasilinear Spaces

Abstract and Applied Analysis ◽

10.1155/2012/951374 ◽

2012 ◽

Vol 2012 ◽

pp. 1-10 ◽

Cited By ~ 4

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.

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