Fixed Point Theorem and its Properties in Cone

Abstract

In this paper we prove some fixed point theorems in fuzzy cone metric
spaces under some fuzzy cone contractive type conditions. The concept of
metric space by replacing the real numbers with an ordered Banach space,
and proved some fixed point results for nonlinear mappings satisfying
some contraction conditions. After that lots of works were devoted to the
problems on cone metric spaces. The notation of fuzzy cone metric space
which generalized the notation of fuzzy metric space. They also presented
some structural properties of fuzzy cone metric spaces and proved a fixed
point theorem under a fuzzy cone contraction condition. Some fixed point
theorems and common fixed point theorems concerning fuzzy cone metric
spaces were obtained and some more properties for fuzzy cone metric
spaces can be found. The purpose of this paper is to give further study of
fixed point theory in fuzzy cone metric spaces. Some fixed point theorems
are proved under some fuzzy cone contractive type conditions.