loading page

Strong coupled fixed point analysis in fuzzy metric spaces and an application to Urysohn integral equations
  • +3
  • Xiangling Li,
  • Saif Rehman,
  • Sami Khan,
  • Nawab Hussain,
  • Jamshaid Ahmad,
  • Hassen Aydi
Xiangling Li
Hebei University of Architecture

Corresponding Author:[email protected]

Author Profile
Saif Rehman
Gomal University
Author Profile
Sami Khan
Gomal University
Author Profile
Nawab Hussain
King Abdulaziz University
Author Profile
Jamshaid Ahmad
University of Jeddah
Author Profile
Hassen Aydi
Université de Sousse Institut Supérieur d'Informatique et des Technologies de Communication de Hammam Sousse
Author Profile


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 $K_1,K_2:[a,b]^2\times \mathbb{R}\to\mathbb{R}$