Unit:
Department of Primary EducationΤομέας Μαθηματικών και ΠληροφορικήςLibrary of the School of Education
Dissertation committee:
1. Βουδούρη Αγγελική, Καθηγήτρια, ΠΤΔΕ, ΕΚΠΑ
2. Μπαραλής Γεώργιος, Αναπλ. Καθηγητής, ΠΤΔΕ, ΕΚΠΑ
3. Γιαλαμάς Βασίλης, Καθηγητής, ΤΕΑΠΗ, ΕΚΠΑ
4. Ζαράνης Νικόλαος, Αναπλ. Καθηγητής, ΠΤΠΕ, Πανεπιστημίου Κρήτης
5. Κρητικός Εμμανουήλ, Επίκ. Καθηγητής, Τμήμα Διοικητικής Επιστήμης και Τεχνολογίας, Οικονομικό Πανεπιστήμιο Αθηνών
6. Μισαηλίδου Χριστίνα, Λέκτορας, ΠΤΔΕ, ΕΚΠΑ
7. Ψαρομήλιγκος Ιωάννης, Καθηγητής, Τμήμα Διοίκησης Επιχειρήσεων, ΑΕΙ Πειραιά Τ.Τ.
Original Title:
Προβλήματα Συναρτησιακών Εξισώσεων
Translated title:
Problems of Functional Equations
Summary:
This PhD Thesis introduces new functional equations of polynomial type and studies their Hyers-Ulam-Rassias and Ulam-Gavruta-Rassias stability. Chapter 1, reviews and presents the evolution of the Ulam Stability Problem during the last 70 years. We highlight the main theoretical results and tools that researchers in the field discovered. Methods of stability and applications in a variety of fields are also mentioned. In Chapter 2, generalization, and modification of classical quadratic functional equation is examined. Also, two new quadratic functional equations are introduced. In Chapter 3, we present two cubic functional equations and we answer an open problem, posed by J.M Rassias, concerned the α-quartic functional equation in non-Archimedean spaces. Finally in Chapter 4, we deal with mixed type functional equations, especially additive-quadratic equations and study them in various spaces. Also, a capable num-ber of counterexamples are given. Chapter 5 poses some open problems that derived from the research.
Main subject category:
Mathematics
Other subject categories:
Equations
Analysis
Keywords:
Ulam stability, Generalized Hyers-Ulam-Rassias Stability, Mixed type functional equations, Fixed point Theory, Banach spaces.
Number of references:
104
Notes:
The missing functional equation, from abstract ,we denote with mark * and appears in the pdf file.
