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Title:	Some fixed point results in cone, quasi-cone and classical metric spaces
Authors:	Shaddad Fawzia Yahya Mohammed (P58672)
Supervisor:	Mohd Salmi Md Noorani, Prof. Dr.
Keywords:	Fixed point theory.
Issue Date:	17-Feb-2015
Description:	Fixed point theory is one of the most powerful and fruitful tools in many fields of pure and applied sciences. It has enormous applications within as well as outside mathematics. The study of fixed point theory which satisfies certain contractive conditions in metric spaces has been at the center of vigorous research activity in the last decades. We start this research by necessary details, definitions and preliminaries about single-valued maps, multi-valued maps, common fixed points, coupled fixed points, and cone metric spaces. This thesis is composed of three parts. In the first part, we obtain the results of common fixed point for generalized Berinde-type contractions and common fixed point in compact metric spaces. We discuss the existence of fixed points in compact metric spaces and partially ordered metric spaces, and also we obtain some results of coupled fixed point and coupled coincidence point without compatibility. As applications, we present the common solution to Urysohn integral equations and the unique common solution to a system of functional equations. In the second part of this thesis, we investigate the existence of fixed point and common fixed point in cone metric spaces. Additionally, we extend some results of fixed point for multi-valued maps by using sequentially lower semi-continuous and multi-valued maps without using the Hausdorff metric in cone metric spaces. In the third part of this research, we define and study different kinds of Cauchy sequences. Furthermore, we introduce the notion of quasi-cone metric space. At the end, we prove some results of fixed points for single-valued maps and multi-valued maps in quasi-cone metric spaces which extend and generalize many results in literature.,Ph.D
Pages:	131
Call Number:	QA329.9 .S534 2015
Publisher:	UKM, Bangi
Appears in Collections:	Faculty of Science and Technology / Fakulti Sains dan Teknologi

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