Nonlinear iteration method for monotone variational inequality and fixed point problem


	Open access
	Nonlinear iteration method for monotone variational inequality and fixed point problem


	Fixed Point Theory, Volume 20, No. 2, 2019, 663-682, June 1st, 2019 DOI: 10.24193/fpt-ro.2019.2.44 Authors: Yekini Shehu Abstract: Using the subgradient extragradient and Halpern methods, we prove two strong convergence results for finding a solution of a variational inequality problem involving Lipschitz continuous monotone with the Lipschitz constant unknown and the solution is also a fixed point a quasi-nonexpansive mapping in real Hilbert space. Key Words and Phrases: Monotone mappings, subgradient extragradient method, Halpern method, quasi-nonexpansive mapping, strong convergence, Hilbert spaces. 2010 Mathematics Subject Classification: 49J53, 65K10, 49M37, 90C25, 47H10. Published on-line: June 1st, 2019. Abstract pdf Fulltext pdf Back to volume's table of contents