1. UKM Learning and Research Repository
2. PHD Thesis / Tesis PHD
3. Faculty of Science and Technology / Fakulti Sains dan Teknologi

Title:	Some fixed point related results in cone b-metric spaces
Authors:	Sahar Mohammad A. Abusalim (P64755)
Supervisor:	Mohd Salmi Md Noorani, Prof. Dr.
Keywords:	Fixed point theory Cone Metric spaces Dissertations, Academic -- Malaysia Universiti Kebangsaan Malaysia -- Dissertations
Issue Date:	15-Jun-2015
Description:	Fixed point theory is an exciting area that takes place in Mathematics. It started as Banach contraction or Banachs fixed point theorem which appeared in 1922. Then, a lot of developments happened in studying this area and some of them are the idea of cone and ordered cone metric spaces, cone and ordered cone b-metric spaces. In this thesis, we have generalized some types of contractive conditions by replacing the constants in the contractive conditions with functions to prove some common fixed point theorems in cone metric spaces. By the same way, we have proved some tripled fixed point theorems in cone metric spaces under the concept of c-distance with different contractive conditions. Furthermore, we have obtained some tripled coincidence point theorems under c-distance for mappings F : X3 ! X and g : X ! X in case of F(X3) g(X) and g(X) is a complete subspace of X in cone metric spaces. We also have proved the existence and the uniqueness of common tripled fixed point theorems using the same distance and spaces. In addition, we have come with some new fixed point and common fixed point theorems that have been proven in ordered cone b-metric spaces. Furthermore, we have studied some tripled coincidence point and common tripled fixed point theorems forW-compatible mappings in cone b-metric spaces. On the other hand, we have given the definitions of (F; g)-invariant set symbolized as M 2 X6 in cone and ordered cone version. Then, we have proved new tripled coincidence point theorems using that definitions under the notion of c-distance in cone metric spaces. Then, we have applied our results in partially ordered cone metric spaces using the mixed g-monotone definition beside the above definitions and the distance. In addition, we have done proving some new tripled coincidence point theorems for mappings F : X3 ! X and g : X ! X that satisfy interesting properties which known as CLRg and (E-A) properties in cone b-metric spaces. Throughout this thesis, we do not impose the normality condition for the cones, but only the assumption that the cone P is solid, that is intP 6= ;,Ph.D.,Fixed point theory is an exciting area that takes place in Mathematics. It started as Banach contraction or Banachs fixed point theorem which appeared in 1922. Then, a lot of developments happened in studying this area and some of them are the idea of cone and ordered cone metric spaces, cone and ordered cone b-metric spaces. In this thesis, we have generalized some types of contractive conditions by replacing the constants in the contractive conditions with functions to prove some common fixed point theorems in cone metric spaces. By the same way, we have proved some tripled fixed point theorems in cone metric spaces under the concept of c-distance with different contractive conditions. Furthermore, we have obtained some tripled coincidence point theorems under c-distance for mappings F : X3 ! X and g : X ! X in case of F(X3) g(X) and g(X) is a complete subspace of X in cone metric spaces. We also have proved the existence and the uniqueness of common tripled fixed point theorems using the same distance and spaces. In addition, we have come with some new fixed point and common fixed point theorems that have been proven in ordered cone b-metric spaces. Furthermore, we have studied some tripled coincidence point and common tripled fixed point theorems forW-compatible mappings in cone b-metric spaces. On the other hand, we have given the definitions of (F; g)-invariant set symbolized as M 2 X6 in cone and ordered cone version. Then, we have proved new tripled coincidence point theorems using that definitions under the notion of c-distance in cone metric spaces. Then, we have applied our results in partially ordered cone metric spaces using the mixed g-monotone definition beside the above definitions and the distance. In addition, we have done proving some new tripled coincidence point theorems for mappings F : X3 ! X and g : X ! X that satisfy interesting properties which known as CLRg and (E-A) properties in cone b-metric spaces. Throughout this thesis, we do not impose the normality condition for the cones, but only the assumption that the cone P is solid, that is intP 6., Ph.D.
Pages:	153
Publisher:	UKM, Bangi
Appears in Collections:	Faculty of Science and Technology / Fakulti Sains dan Teknologi

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.