Open Access$FG$-coupled fixed point theorems in cone metric spaces
Author(s) -
E. Prajisha,
P. Shaini
Publication year - 2018
Publication title -
karpatsʹkì matematičnì publìkacìï
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.63
H-Index - 4
eISSN - 2313-0210
pISSN - 2075-9827
DOI - 10.15330/cmp.9.2.163-170
Subject(s) - mathematics , fixed point theorem , uniqueness , fixed point , metric space , coincidence point , type (biology) , contraction (grammar) , generalization , cone (formal languages) , contraction mapping , schauder fixed point theorem , discrete mathematics , pure mathematics , mathematical analysis , combinatorics , brouwer fixed point theorem , algorithm , medicine , ecology , biology
The concept of $FG$- coupled fixed point introduced recently is a generalization of coupled fixed point introduced by Guo and Lakshmikantham. A point $(x,y)\in X\times X$ is said to be a coupled fixed point of the mapping $F: X\times X \rightarrow X$ if $F(x,y)=x$ and $F(y,x)=y$, where $X$ is a non empty set. In this paper, we introduce $FG$- coupled fixed point in cone metric spaces for the mappings $F:X\times Y \rightarrow X$ and $G:Y\times X\rightarrow Y$ and establish some $FG$- coupled fixed point theorems for various mappings such as contraction type mappings, Kannan type mappings and Chatterjea type mappings. All the theorems assure the uniqueness of $FG$- coupled fixed point. Our results generalize several results in literature, mainly the coupled fixed point theorems established by Sabetghadam et al. for various contraction type mappings. An example is provided to substantiate the main theorem.