Metric Fixed Point Theory: Old Problems and New Directions
نویسندگان
چکیده
This is a brief review of some of the things, both past and present, which have motivated the writer’s interest in metric fixed point theory.
منابع مشابه
Some Fixed Point Results on Intuitionistic Fuzzy Metric Spaces with a Graph
In 2006, Espinola and Kirk made a useful contribution on combining fixed point theoryand graph theory. Recently, Reich and Zaslavski studied a new inexact iterative scheme for fixed points of contractive and nonexpansive multifunctions. In this paper, by using the main idea of their work and the idea of combining fixed point theory on intuitionistic fuzzy metric spaces and graph theory, ...
متن کاملFixed point theory in generalized orthogonal metric space
In this paper, among the other things, we prove the existence and uniqueness theorem of fixed point for mappings on a generalized orthogonal metric space. As a consequence of this, we obtain the existence and uniqueness of fixed point of Cauchy problem for the first order differential equation.
متن کاملCommon Fixed Point Theorems for Weakly Compatible Mappings by (CLR) Property on Partial Metric Space
The purpose of this paper is to obtain the common fixed point results for two pair of weakly compatible mapping by using common (CLR) property in partial metric space. Also we extend the very recent results which are presented in [17, Muhammad Sarwar, Mian Bahadur Zada and Inci M. Erhan, Common Fixed Point Theorems of Integral type on Metric Spaces and application to system of functional equat...
متن کاملCoupled fixed point on ordered cone metric spaces with application in integral equations
Our theorems are on ordered cone metric spaces which are not necessarily normal. In the end, we describe the application of the main results in the integral equation.Although Du in [W. S. Du, A note on cone metric fixed point theory and its equivalence, Nonlinear Analysis, 72(2010) 2259-2261.], showed that the fixed point results in the setting of cone...
متن کاملFixed point theory for cyclic $varphi$-contractions in fuzzy metric spaces
In this paper, the notion of cyclic $varphi$-contraction in fuzzymetric spaces is introduced and a fixed point theorem for this typeof mapping is established. Meantime, an example is provided toillustrate this theorem. The main result shows that a self-mappingon a G-complete fuzzy metric space has a unique fixed point if itsatisfies the cyclic $varphi$-contraction. Afterwards, some results inco...
متن کامل