Approximation methods for a common minimum-norm point of a solution of variational inequality and fixed point problems in Banach spaces
Bull. Korean Math. Soc. 2014 Vol. 51, No. 3, 773-788
https://doi.org/10.4134/BKMS.2014.51.3.773
Published online May 31, 2014
N. Shahzad and H. Zegeye
King Abdulaziz University, University of Botswana
Abstract : We introduce an iterative process which converges strongly to a common minimum-norm point of solutions of variational inequality problem for a monotone mapping and fixed points of a finite family of relatively nonexpansive mappings in Banach spaces. Our theorems improve most of the results that have been proved for this important class of nonlinear operators.
Keywords : monotone mappings, relatively nonexpansive mappings, strong convergence, variational inequality problems
MSC numbers : 47H05, 47H09, 47H10, 47J05, 47J25
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