Research Information System
Thesis Type: Doctorate
Institution Of The Thesis: Gazi University, Fen Bilimleri Enstitüsü, Turkey
Approval Date: 2022
Thesis Language: Turkish
Student: ÇETİN CEMAL ÖZEKEN
Supervisor: Cüneyt Çevik
Abstract:
The main purpose of this thesis is to generalize the fixed point results obtained in metric spaces and ordered metric spaces with approaches different than the ones in the literature, on ordered vector metric spaces and hence to make the obtained results applicable for wider classes of functions. These generalizations are obtained not only by changing the space structure but also by stretching the contraction conditions, changing the topological structures of the functions, and altering the conditions on the variables during the establishment of the iterative method. In this work firstly, fixed point results for orderpreserving and order-reversing functions on ordered vector metric spaces are obtained. Then, the coupled fixed point results are obtained for functions having mixed monotone property on ordered vector metric spaces. In the same chapter, functions having double monotone property are defined and the results obtained for functions having mixed monotone property are reinterpreted for these functions. Then, the mentioned results are expanded for functions not having any type of monotonicity property. In the next chapter, the definitions of ordered vector quasi-contraction and ordered vectorial almost-contraction are given, and fixed-point results are presented for vectorial almost-contraction. In the last section, fixed point results are obtained for ordered vectorial Prešić contractions on finite products of ordered vector metric spaces. In each chapter the relationships between the results obtained as well as between other studies in the literature are clearly emphasized with examples and notes.
Key Words : Ordered vector space, Riesz space, vector metric space, ordered vector
metric space, fixed point, coupled fixed point, mixed monotone
function, double monotone function, ordered vectorial quasi contraction,
ordered vectorial almost contraction, ordered vectorial Prešić type
contraction