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Title:	On cone metric spaces with generalized distance in fixed point theory
Authors:	Zaid Mohammed Hussein Fadail (P62505)
Supervisor:	Abd. Ghafur Ahmad, Assoc. Prof. Dr.
Keywords:	Fixed point theory Coincidence theory (Mathematics) Universiti Kebangsaan Malaysia -- Dissertations Dissertations, Academic -- Malaysia
Issue Date:	22-May-2014
Description:	Fixed point theory is one of the most powerful and fruitful tools of modern mathematics and may be considered a core subject of nonlinear analysis started by Banach in 1922. A cone metric space introduced as a generalization of a metric space in 2007. In this thesis, we are going to continue the study in fixed point theory but now in cone metric spaces, cone metric spaces with generalized distance and cone b-metric spaces. We started this research by recalling the history and the developments of this subject. Then, the objectives of the research were discussed and explained. We presented some definitions and results for this area that are needed for our work. Our first results has begun to prove the existence and uniqueness of the coincidence point of N-order and common fixed point of N-order for WN- compatible mappings in a cone metric space. Consequently, a fixed point theorem of N-order is obtained. Furthermore, we discussed some spacial cases for N = 2; 3 to obtain a common coupled fixed point theorem, a coupled fixed point theorem, a common tripled fixed point theorem and a tripled fixed point theorem in cone metric spaces. Under the concept of the c-distance in a cone metric space, our work is divided into two parts. In the first part, we proved a common fixed point theorem for weakly compatible mappings without assumption of normality for cones . Then, we obtained a fixed point theorem for self-mappings. Next, we proved the existence and uniqueness of the coupled coincidence point and the common coupled fixed point for W2-compatible mappings without assumptions of normality for cones and continuity condition for maps. After that, we presented a coupled fixed point theorem. In the second part, we generalized some well-known contractive conditions in literature by replacing the constant numbers in that with functions. Using this generalization with more properties for these functions, we proved some fixed point theorems, coupled fixed point theorems and common coupled fixed point theorems. Our final work was in a cone b-metric space, we established coupled coincidence point and common coupled fixed point theorems for W2-compatible mappings. In addition, we obtained a coupled fixed point theorem in such space.,Ph.D.
Pages:	122
Publisher:	UKM, Bangi
Appears in Collections:	Faculty of Science and Technology / Fakulti Sains dan Teknologi

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