# A Coupled Fixed Point Problem Under a Finite Number of Equality Constraints

• Praveen Agarwal
• Mohamed Jleli
• Bessem Samet
Chapter

## Abstract

Let $$(E,\Vert \cdot \Vert )$$ be a Banach space with a cone P. Let $$F,\varphi _i: E\times E\rightarrow E$$ ($$i=1,2,\ldots ,r$$) be a finite number of mappings. In this chapter, we provide sufficient conditions for the existence and uniqueness of solutions to the problem: Find $$(x,y)\in E\times E$$ such that
\begin{aligned} \left\{ \begin{array}{lll} F(x,y)&{}=&{}x,\\ F(y,x)&{}=&{}y,\\ \varphi _i(x,y)&{}=&{}0_E,\,\, i=1,2,\ldots ,r, \end{array} \right. \end{aligned}
where $$0_E$$ is the zero vector of E. The main reference for this chapter is the paper [4].

## References

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Jleli, M., Samet, B.: A Coupled fixed point problem under a finite number of equality constraints in a Banach space partially ordered by a cone. Fixed Point Theory (in Press)Google Scholar