A coupled fixed point problem under a finite number of equality constraints in a Banach space partially ordered by a cone


	Open access
	A coupled fixed point problem under a finite number of equality constraints in a Banach space partially ordered by a cone


	Fixed Point Theory, Volume 19, No. 2, 2018, 611-624, June 1st, 2018 DOI: 10.24193/fpt-ro.2018.2.48 Authors: Mohamed Jleli and Bessem Samet Abstract: Let $(E,\\|\cdot\\|)$ be a Banach space with a cone P. Let $F,\varphi_i: E\times E\to E (i=1,2,\ldots,r)$ be a finite number of mappings. We obtain sufficient conditions for the existence and uniqueness of solutions to the problem $\left\{\begin{array}{lll} F(x,y)&=&x,\\ F(y,x)&=&y,\\ \varphi_i(x,y)&=&0_E,\,\, i=1,2,\ldots,r, \end{array} \right.$ where 0_E is the zero vector of E. Key Words and Phrases: Coupled fixed point, equality constraints, Banach space, cone, partial order. 2010 Mathematics Subject Classification: 47H10, 47H07. Published on-line: June 1st, 2018. Abstract pdf Fulltext pdf Back to volume's table of contents