| Ders Adı | Kodu | Yarıyıl | T+U Saat | Kredi | AKTS |
|---|---|---|---|---|---|
| Fixed Point Theory II İn Metric Spaces | MAT 528 | 0 | 3 + 0 | 3 | 6 |
| Ön Koşul Dersleri | Fixed Point Theory in Metric Spaces I |
| Önerilen Seçmeli Dersler | |
| Dersin Dili | Türkçe |
| Dersin Seviyesi | YUKSEK_LISANS |
| Dersin Türü | Seçmeli |
| Dersin Koordinatörü | Doç.Dr. AYNUR ŞAHİN |
| Dersi Verenler | |
| Dersin Yardımcıları | |
| Dersin Kategorisi | Alanına Uygun Öğretim |
| Dersin Amacı | The undertanding of fixed point theory in Banach spaces, the learning of fixed point theory in Banach lattices and metric fixed point theory, the knowing of Banach space ultrapowers and their properties |
| Dersin İçeriği | Banach space, Hahn-Banach theorem, uniform convexity and reflexivity, the basic fixed point theorems in Banach spaces, metric fixed point theory, stability results in arbitrary spaces, the Goebel-Karlovitz lemma, orthogonal convexity, asymptotically regular mappings, Banach lattices, fixed point theory in Banach lattices, Banach space ultrapowers and their properties, some fixed point theorems in Banach spaces ultrapowers |
| # | Ders Öğrenme Çıktıları | Öğretim Yöntemleri | Ölçme Yöntemleri |
|---|---|---|---|
| 1 | He/She recognizes the basic fixed point theorems in Banach spaces. | Drilland Practice, Self Study, Problem Solving, | Testing, Homework, Performance Task, |
| 2 | He/She interprets the metric fixed point theory. | Lecture, Question-Answer, Drilland Practice, Self Study, Problem Solving, | Testing, Homework, Performance Task, |
| 3 | He/She learns the fixed point theory in Banach lattices. | Question-Answer, Drilland Practice, Self Study, Problem Solving, Lecture, | Performance Task, Testing, Homework, |
| 4 | He/She knowns Banach space ultrapowers and their properties. | Question-Answer, Drilland Practice, Self Study, Problem Solving, Lecture, | Performance Task, Testing, Homework, |
| Hafta | Ders Konuları | Ön Hazırlık |
|---|---|---|
| 1 | Banach space, convexity, the modulus of convexity | |
| 2 | Hahn-Banach theorem, weak and weak* topologies and some their properties | |
| 3 | Schur property, uniform convexity and reflexivity | |
| 4 | The basic fixed point theorems in Banach spaces | |
| 5 | Banach algebra: Stone-Weierstrass theorem | |
| 6 | Metric fixed point theory | |
| 7 | Stability results in arbitrary spaces | |
| 8 | Midterm exam | |
| 9 | The Goebel-Karlovitz lemma, orthogonal convexity | |
| 10 | Asymptotically regular mappings | |
| 11 | Banach lattices | |
| 12 | The fixed point theory in Banach lattices | |
| 13 | Banach space ultrapowers and their properties | |
| 14 | Some fixed point theorems in Banach spaces ultrapowers |
| Kaynaklar | |
|---|---|
| Ders Notu | |
| Ders Kaynakları | 1) K. Goebel, W.A. Kirk, Topics in Metric Fixed Point Theory, Cambridge University Press, 1990. 2) M.R. Bridson, A. Haefliger, Metric Spaces of Non-Positive Curvature, Springer, 1991. 3) M.A. Khamsi, W.A. Kirk, An Introduction to Metric Spaces and Fixed Point Theory, Pure and Applied Mathematics, A Wiley-Intersicence Series of Texts, Monographs and Tracks, 2001. |
| Sıra | Program Çıktıları | Katkı Düzeyi | |||||
|---|---|---|---|---|---|---|---|
| 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 | ||||||
| 2 | Student follows the current journals in his/her field and puts forward problems. | X | |||||
| 3 | Student understands the relations between the disciplines pertaining to the undergraduate programs of Mathematics | X | |||||
| 4 | Student gets new knowledge by relating the already acquired experience and knowledge with the subject-matters out of his/her field. | X | |||||
| 5 | Student uses different proof methods to come to a solution by analyzing the problems encountered. | ||||||
| 6 | Student determines the problems to be solved within his/her field and if necessary takes the lead. | X | |||||
| 7 | Student conveys, in team work, his/her knowledge in the studies done in different disciplines by applying the dynamics pertaining to his/her own field. | ||||||
| 8 | Student critically evaluates the knowledge got at the bachelor´s degree level, makes up the missing knowledge and focuses on the current subject-matters | X | |||||
| 9 | Student knows a foreign language to communicate orally and in writing and uses the foreign language in a way that he/she can have a command of the Maths terminology and can do a source research. | X | |||||
| 10 | Student improves himself/herself at a level of expertness in Mathematics or in the fields of application by improving the knowledge got at the bachelor´s degree level. | ||||||
| 11 | Student considers the scientific and cultural ethical values in the phases of gathering and conveying data or writing articles. | ||||||
| Değerlendirme Sistemi | |
|---|---|
| Yarıyıl Çalışmaları | Katkı Oranı |
| 1. Ara Sınav | 70 |
| 1. Ödev | 15 |
| 2. Ödev | 15 |
| Toplam | 100 |
| 1. Final | 50 |
| 1. Yıl İçinin Başarıya | 50 |
| Toplam | 100 |
| AKTS - İş Yükü Etkinlik | Sayı | Süre (Saat) | Toplam İş Yükü (Saat) |
|---|---|---|---|
| Course Duration (Including the exam week: 16x Total course hours) | 16 | 3 | 48 |
| Hours for off-the-classroom study (Pre-study, practice) | 14 | 1 | 14 |
| Mid-terms | 1 | 24 | 24 |
| Assignment | 2 | 8 | 16 |
| Final examination | 1 | 48 | 48 |
| Toplam İş Yükü | 150 | ||
| Toplam İş Yükü / 25 (Saat) | 6 | ||
| Dersin AKTS Kredisi | 6 | ||