Coupled coincidence point and coupled common fixed point theorems in partially ordered metric spaces with \(w\)-distance (Q610884)

Let \(X\) be a nonempty set and \(F:X\times X\rightarrow X\), \(g:X\rightarrow X\) be two mappings. An ordered pair \((x,y)\in X\times X\) is called: (i) a coupled coincidence point of \(\{F,g\}\) if \(g(x)=F(x,y)\) and \(g(y)=F(y,x)\); (ii) a common coupled coincidence point of \(\{F,g\}\) if \(x=g(x)=F(x,y)\) and \(y=g(y)=F(y,x)\). This paper gives some coupled coincidence/fixed point theorems in a metric space \((X,d)\) endowed with a \(w\)-distance and a partial order, using a weak contractive type assumption.