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

Praveen Agarwal (), Mohamed Jleli and Bessem Samet
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Praveen Agarwal: Anand International College of Engineering, Department of Mathematics
Mohamed Jleli: King Saud University, Department of Mathematics, College of Sciences
Bessem Samet: King Saud University, Department of Mathematics, College of Sciences

Chapter Chapter 8 in Fixed Point Theory in Metric Spaces, 2018, pp 123-138 from Springer

Abstract: 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 finiteConstraint 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].

Keywords: Fixed Point Results; Zero Vector; Banach Space; Main Reference; Abstract Harmonic Analysis (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-13-2913-5_8

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DOI: 10.1007/978-981-13-2913-5_8

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