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Course Information
Course Unit Title : The Types of Convergence in Topology and Analysis
Course Unit Code : 01MAT9621
Type of Course Unit : Optional
Level of Course Unit : Second Cycle
Year of Study : Preb
Semester : 255.Semester
Number of ECTS Credits Allocated : 6,00
Name of Lecturer(s) : ---
Course Assistants : ---
Learning Outcomes of The Course Unit : Theory of Classical Convergence
Theory of Statistical Convergence
Theory of Ideal Convergence
and the others
Mode of Delivery : Face-To-Face
Prerequisities and Co-requisities Courses : Unavailable
Recommended Optional Programme Components : Unavailable
Course Contents : The basic teories of classical convergence, statistical convergence, ideal convergence, A-statistical convergence, lacunary and lacunary statistical convergence, lambda and lambda-statistical convergence. The sets of limit points and cluster points related with these convergence are investigated.
Languages of Instruction : Turkish-English
Course Goals : To give new types of convergence
Course Aims : To give some new types of convergence in literature
WorkPlacement   Not Available
Recommended or Required Reading
Textbook : CONNOR, J.? GANICHEV, M.? KADETS, V.: A characterization of
Banach spaces with separable duals via weak statistical convergence, J.
Math. Anal. Appl. 244 (2000), 251-261.

CONNOR, J.? GROSSE ERDMANN, K.G.: Sequential definitions of continuity
for real functions, Rocky Mountain J. Math. 33 (2003), 93-121.

FAST, H.: Sur la convergence statistique, Colloq. Math. 2 (1951), 241-244.

FRIDY, J. A.: On statistical convergence, Analysis 5 (1985), 301-313.
Additional Resources : KOLK, E.: The statistical convergence in Banach spaces, Acta Et Commentationes
Unv. Tartuensis 928 (1991), 41-52.

MAMEDOV, M. A.? PEHLIVAN, S.: Statistical cluster points and turnpike
theorem in nonconvex problems, J. Math. Anal. Appl. 256 (2001), 686-
693.

NIVEN, I.? ZUCKERMAN, H. S.? MONTGOMERY, H. L.: An Introduction
to the Theory of Numbers, John Wiley & Sons, New York, 1991.

?ALÁT, T.: On statistically convergent sequences of real numbers, Math.
Slovaca 30 (1980), 139-150.

STEINHAUS, H.: Sur la convergence ordinaire et la convergence asymptotique,
Colloq. Math. 2 (1951), 73-74.

TRIPATHY, B. C.: On statistically convergent sequences, Bull. Cal. Math.
Soc. 90 (1998), 259-262
Material Sharing
Documents :
Assignments :
Exams :
Additional Material :
Planned Learning Activities and Teaching Methods
Lectures, Practical Courses, Presentation, Seminar, Project, Laboratory Applications (if necessary)
ECTS / Table Of Workload (Number of ECTS credits allocated)
Student workload surveys utilized to determine ECTS credits.
Activity :
Number Duration Total  
Course Duration (Excluding Exam Week) :
14 3 42  
Time Of Studying Out Of Class :
14 5 70  
Homeworks :
3 15 45  
Presentation :
0 0 0  
Project :
0 0 0  
Lab Study :
0 0 0  
Field Study :
0 0 0  
Visas :
1 15 15  
Finals :
1 15 15  
Workload Hour (30) :
30  
Total Work Charge / Hour :
187  
Course's ECTS Credit :
6      
Assessment Methods and Criteria
Studies During Halfterm :
Number Co-Effient
Visa :
1 50
Quiz :
0 0
Homework :
3 50
Attendance :
0 0
Application :
0 0
Lab :
0 0
Project :
0 0
Workshop :
0 0
Seminary :
0 0
Field study :
0 0
   
TOTAL :
100
The ratio of the term to success :
50
The ratio of final to success :
50
TOTAL :
100
Weekly Detailed Course Content
Week Topics  
1 The basic theorems related with classical convergence
 
2 The basic theorems related with statistical convergence
 
3 The basic theorems related with ideal convergence
 
4 The basic theorems related with A-statistical convergence
 
5 The basic theorems related with lacunary and lacunary statistical convergence
 
6 The basic theorems related with lambda and lambda-statistical convergence
 
7 The sets of limit points and cluster points
 
8 Uniform and uniform statisatical convergence of sequence of functions
 
9 Alpha and statisatical alpha-convergence of sequence of functions
 
10 Ideal convergence of sequence of functions
 
11 Ideal alpha-convergence of sequence of functions
 
12 The properties of equicontinuity and exhaustiveness of sequence of functions
 
13 The theorems related with equicontinuity and exhaustiveness
 
14 Filter convergence
 
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