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Title:	Fixed point results for certain types of weak contraction mappings on various metric spaces
Authors:	Rahma Zuhra (P70794)
Supervisor:	Mohd Salmi Md Noorani, Prof. Dr.
Keywords:	Banach spaces Metric spaces Universiti Kebangsaan Malaysia -- Dissertations Dissertations, Academic -- Malaysia
Issue Date:	16-Aug-2018
Description:	The Banach contraction mapping principle is the most fundamental result in fixed point theory. This principle will guarantee the existence and the uniqueness of fixed points on different metric spaces. There are numerous researches which deal with extensions and generalizations of Banach's theorem in pure and applied analysis. Nowadays, the study of weak contraction principle which satisfies certain conditions in metric spaces has been widely developed. In addition, partially ordered properties have involved in the research to ensure the existence of each element in metric space. In this research, we use three different metric spaces, i.e. quasi metric space, cone metric space and tvs-cone metric space. We also utilize three types of metrics that are: ordinary metric, w-distance, and c-distance where every type is exercising four configurations of the metrics according to its metric spaces. Then, these metrics equipped with weak contraction mappings, and the existences of fixed points of the mappings are summarized into theorems that will be proved. In this thesis, we begin by recalling the notions and preliminaries concepts related to the research topic. Our results have proved the existence of fixed points and common fixed points in partially ordered quasi metric spaces for the four configurations. Next, we provided a fixed point and a common fixed point of certain weak contraction mappings with w-distance in partially ordered quasi metric spaces. By the fact that a fixed point of any map can be viewed as a common fixed point of that mapping, we have proved by a shorter way the existence of the common fixed point in quasi metric spaces. Then, we also have applied an application of the fixed point theorems in an ordinary differential equation in quasi metric spaces. Afterwards, we generalized the existence of a multidimensional fixed point and a common fixed point in partially ordered quasi metric spaces. Finally, we have generalized some contraction conditions in the previous works by replacing the constant with functions.Then, we have transferred the generalization to prove the fixed point and the common fixed point concerning to c-distance in partially ordered cone metric spaces and in partially ordered tvs-cone metric spaces.,'Certification of Master's/Doctoral Thesis' is not available,Ph.D.
Pages:	142
Call Number:	QA322.2.Z834 2018 tesis
Publisher:	UKM, Bangi
Appears in Collections:	Faculty of Science and Technology / Fakulti Sains dan Teknologi

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