Set-Valued Analysis [MATH-774]

MATH-774 Set-Valued Analysis

Description

This course is devoted to a compressed and self-contained exposition of an important part of contemporary mathematics: set-valued analysis.The great attention is paid also to measurable set-valued functions, continuous, Lipschitz and some special types of selections, fixed point and coincidence theorems, covering set-valued maps, topological degree theory and differential inclusions.

Learning Outcomes

After successful completion of the course, students are able to apply the theory of set-valued mappings, Upper and lower semicontinuous of set-valued maps, Hausdorff-Pompeiu distance. fixed point theorems, integral of set-valued functions, the theory of differential inclusions, selection theorems and measurable multifunctions.

Contents

Preliminaries,
Hausdorff - Pompeiu metric,
Upper and lower semicontinuous,
Multifunctions,
Hausdorff-Pompeiu continuity,
Closed multifunctions, continuous,
Selections, measurable multifunctions,
Aumann integral, Hukuhara derivative.

Recommended Books

Jean Pierre Aubin, Hélène Frankowska, Set-Valued Analysis(Systems & Control: Foundations & Applications), Birkhauser Boston, (1990).
Enayet U Tarafdar and Mohammad S R Chowdhury, Topological Methods for Set-Valued Nonlinear Analysis, World Scientific Publishing Co. Pte. Ltd., (2008).

Suggested Books

Guang-ya Chen, Xuexiang Huang, Xiaogi Yang, Vector optimization: Set-valued and variational analysis, Springer-Verlag Berlin Heidelberg (2005).

2. V. Lakshmikatham, T. G. Bhaskar, and J. V. Devi, Theory of Set Differential equations in Metric Spaces, Cambridge Scientic, Cambridge, UK, (2006).

Assessment Criteria

Sessional: 20 (Presentation / Assignment 10, Attendance 05, Quiz 05)

Mid-Term Exam: 30

Final-Term Exam: 50