Ishikawa iterations for equilibrium and fixed point problems for nonexpansive mappings in Hilbert spaces
Filomena Cianciaruso, Giuseppe Marino, Luigi Muglia · 2008
In this paper, we introduce an iterative scheme Ishikawa-type for finding a common element of the set EP(G) of the equilibrium points of a bifunction G and the set Fix(T) of fixed points of a nonexpansive mapping T in a Hilbert space H. We prove that the method converges strongly to an element z 2 Fix(T) EP(G) which is the unique solution of the variational inequality h(A f )z,x zi 0 for every x 2 Fix(T) EP(G). The results presented here are situated on the line of research of (5, 6, 7, 10, 12, 13).