Strong coupled fixed point analysis in fuzzy metric spaces and an
application to Urysohn integral equations
Abstract
The aim of this paper is to establish some strong coupled fixed point
theorems via a new concept of cyclic contractive type mappings in the
context of fuzzy metric spaces. Moreover, we ensure the existence of a
common solution of the two Urysohn type integral equations:% for our
result to get the existence theorem for common solution. The two Urysohn
type integral equations are \begin{align*}
&\xi(l)=\int_{a}^{b}K_1(l,s,\xi(s))ds+h_1(l),\\
&\xi(l)=\int_{a}^{b}K_2(l,s,\xi(s))ds+h_2(l),
\end{align*} where
$l\in[a,b]\subset\mathbb{R}$,
$\xi,h_1,h_2\in
C([a,b],\mathbb{R})$ and
$K_1,K_2:[a,b]^2\times
\mathbb{R}\to\mathbb{R}$