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Strong coupled fixed point analysis in fuzzy metric spaces and an application to Urysohn integral equations
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  • Xiangling Li,
  • Saif Rehman,
  • Sami Khan,
  • Nawab Hussain,
  • Jamshaid Ahmad,
  • Hassen Aydi
Xiangling Li
Hebei University of Architecture
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Saif Rehman
Gomal University
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Sami Khan
Gomal University
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Nawab Hussain
King Abdulaziz University
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Jamshaid Ahmad
University of Jeddah
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Hassen Aydi
Université de Sousse Institut Supérieur d'Informatique et des Technologies de Communication de Hammam Sousse
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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 $K_1,K_2:[a,b]^2\times \mathbb{R}\to\mathbb{R}$