Fuzzy contraction mappings and fixed points

ivFUZZY CONTRACTION MAPPINGS AND FIXED POINTS(Ph. D. Thesis )Cihangir ALACAGAZI UNIVERSITYINSTUTE OF SCIENCE AND TECHNOLOGYMarch 2006ABSTRACTIn this thesis, we define and introduce the compatible maps and the compatiblemaps of types (α) and (β) in intuitionistic fuzzy metric spaces first time inliterature. We investigate some fundamental relations between these kind ofmappings. Furthermore, we give an original definition of the commutative mapsand we find a relation between commutative maps and compatible maps inintuitionistic fuzzy metric spaces. Finally, we prove two original common fixedpoint theorems for the concept of compatibility and we give a sample whichsupports to the first main theorem.Science Code: 204.1.132Key Words : Fuzzy set, Fuzzy metric space, Complete space, Cauchysequence, Intuitionistic fuzzy metric space, Commutativemapping, Compatible mapping, Compatible mappings of types(α) and (β), Fixed pointPage Number : 61Adviser : Prof. Dr. Cemil YILDIZ