Course Name Code Semester T+U Hours Credit ECTS
Fixed Point Theory and Its Applications II MAT 626 0 3 + 0 3 6
Precondition Courses Topology I-II, Functional Analysis I-II
Recommended Optional Courses
Course Language Turkish
Course Level Doctorate Degree
Course Type Optional
Course Coordinator Doç.Dr. MAHPEYKER ÖZTÜRK
Course Lecturers Doç.Dr. MAHPEYKER ÖZTÜRK,
Course Assistants
Course Category
Course Objective To comprehend the fixed point theory in normed spaces.
To learn the geometric constants in Banach spaces.
To understand the...to fixed point and iteration methods.
Course Content Fixed Point Concept in Normed Spaces and Contraction Mapping Principle, Applications of Banach Fixed Point Theorem in Normed Spaces, Non-expansive Mappings, The basic fixed point theorems for non-expansive mappings, Uniformly L-Lipschitzin and Non Lipschitzian Mappings, Brouwers and Schauders Theorems, Topological fixed point theorems and hyperconvexity, Geometric Coefficients of Banach Spaces, Asymptotic centers and asymptotic Radius, The Opial and uniform Opial conditions, Normal structure, Normal structure coefficient, Weak normal structure coefficient, Maluta constant, Approximation to the Fixed Points and Iterations Methods
# Course Learning Outcomes Teaching Methods Assessment Methods
1 He\she explains the concept of fixed point and contraction mapping principle in normed spaces Lecture, Problem Solving, Testing, Homework,
2 He\she comprehends the applications of Banach fixed point theorems in normed spaces Lecture, Question-Answer, Problem Solving, Testing, Homework,
3 He\she explains non-expansive mappings and fundamental fixed point theorems for non-expansive mappings Lecture, Question-Answer, Problem Solving, Testing, Homework,
4 He\she conceives uniformly L-Lipschitzian mappings and non-Lipschitzian mappings Lecture, Question-Answer, Problem Solving, Testing, Homework,
5 He\she comments Brouwer fixed point theorem and Schauder fixed point theorem Lecture, Question-Answer, Problem Solving, Testing, Homework,
6 He\she explains topological fixed point theorems and hyperconvexity Lecture, Question-Answer, Problem Solving, Testing, Homework,
7 He\she explains geometric constants , Asymptotic center and asymptotic radius,Opial and uniformly Opial conditions,Normal Structure and Normal Structure constant, Weakly Normal Structure Constant and Maluta Constant in Banach spaces. Lecture, Question-Answer, Problem Solving, Testing, Homework,
8 He\she comments approximations to the fixed point and iteration methods. Lecture, Question-Answer, Problem Solving, Testing, Homework,
Week Course Topics Preliminary Preparation
1 Banach contraction mapping principle and fixed point theory in normed spaces
2 Applications of Banach fixed point theorem in normed spaces
3 Non-expansive mappings
4 Fundamental fixed point theorems for non-expansive mappings
5 Uniformly L-Lipschitzian and non-Lipschitzian mappings
6 Brouwer Theorem-Schauder Theorem
7 Topological fixed point theorems and Hyperconvexity
8 Mid-term exam
9 Geometric constants in Banach spaces
10 Asymptotic center and asymptotic radius
11 Opial and uniformly Opial conditions
12 Normal Structure and Normal Structure constant
13 Weakly Normal Structure Constant and Maluta Constant
14 Approximations to the fixed point and iteration methods
Resources
Course Notes
Course Resources 1. The Computation of Fixed Points and Its Applications,1976
2. Topics in Metric Fixed Point Theory, 1990
3. Handbook of Metric Fixed Point Theory,2001
4. An Introduction to Metric Spaces and Fixed Point Theory, 2001
5. Fixed Point Theory, 2003
6. Homotopy Methods in Topological Fixed and Periodic Points Theory,2006
7. Fixed Point Theory for Lipschitzian-type Mappings with Applications,2009
8. Fixed Point Theory in Ordered Sets and Applications,2010
Order Program Outcomes Level of Contribution
1 2 3 4 5
0 Develop strategic, political and practice plans and evaluate the results by taking into account the quality process in his/her area of expertise
1 At a master´s degree level, student reaches new knowledge via scientific researches, the use of knowledge of the same field as him/her or of different field from him/her, and the use of knowledge based on the competence in his/her field; s/he interprets the knowledge and prospects for the fields of application. X
2 Student completes the missing or limited knowledge by using the scientific methods. X
3 Student freely poses a problem of his/her field, develops a solution method, solves the problem, and evaluates the result. X
4 Student conveys, orally or in writing, his/her studies or the current developments in his/her field to the people in or out of his/her field. X
5 Student finds a solution to the unforeseen complex problems in his/her studies by developing new approaches. X
6 At a doctorate degree level, student prepares at least one scientific article of his/her field to be published in an international indexed journal, and s/he extends its popularity. X
7 Student analyzes the works that have been published before, approaches the same subjects with different proof methods, or determines the open problems about the current subject matters. X
8 Student looks for the scientists studying on the same field as him/her, and s/he gets in touch with them for a collaborative work. X
9 Student knows enough foreign language to do a collaborative work with the scientists studying on the same field as him/her abroad. X
10 Student follows the necessary technological developments in his/her field, and s/he uses them. X
11 Student looks out for the scientific and ethic values while gathering, interpreting and publishing data. X
Evaluation System
Semester Studies Contribution Rate
1. Ara Sınav 80
1. Ödev 10
2. Ödev 10
Total 100
1. Yıl İçinin Başarıya 50
1. Final 50
Total 100
ECTS - Workload Activity Quantity Time (Hours) Total Workload (Hours)
Course Duration (Including the exam week: 16x Total course hours) 16 3 48
Hours for off-the-classroom study (Pre-study, practice) 16 3 48
Mid-terms 1 20 20
Assignment 2 5 10
Final examination 1 20 20
Performance Task (Seminar) 1 10 10
Total Workload 156
Total Workload / 25 (Hours) 6.24
dersAKTSKredisi 6