We introduce a new iterative algorithm for finding a common element of a fixed point problem of amenable semigroups of nonexpansive mappings, the set solutions of a system of a general system of generalized equilibria in a real Hilbert space. Then, we prove the strong convergence of the proposed iterative algorithm to a common element of the above three sets under some suitable conditions. As applications, at the end of the paper, we apply our results to find the minimum-norm solutions which solve some quadratic minimization problems. The results obtained in this paper extend and improve many recent ones announced by many others.
"A New Computational Technique for Common Solutions between Systems of Generalized Mixed Equilibrium and Fixed Point Problems." J. Appl. Math. 2013 (SI21) 1 - 17, 2013. https://doi.org/10.1155/2013/230392