### 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

1. Preliminaries,
2. Hausdorff - Pompeiu metric,
3. Upper and lower semicontinuous,
4. Multifunctions,
5. Hausdorff-Pompeiu continuity,
6. Closed multifunctions, continuous,
7. Selections, measurable multifunctions,
8. Aumann integral, Hukuhara derivative.

Recommended Books

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

Suggested Books

1. 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

### Key Dates and Time of Class Meeting

Wednesday                                             11:00 AM-12:30 PM

Thursday                                                 09:30 AM-11:00 AM

Commencement of Classes                    March 02, 2020

Mid Term Examination                             April 27 to May 04, 2020

Final Term Examination                           June 22-26, 2020

Declaration of Result                               July 03, 2020