 
Summary: JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS: Vol. 108, No. 3, pp. 527541, MARCH 2001
Iterative Schemes for Solving Mixed
VariationalLike Inequalities1,2
Q. H. ANSARI
3
AND J. C. YAO
4
Communicated by S. Schaible
Abstract. In the present paper, we introduce the concept of cocoer
civity of a map and develop some iterative schemes for finding the
approximate solutions of mixed variationallike inequalities. We use the
concept of cocoercivity to prove the convergence of the approximate
solutions to the exact solution of mixed variationallike inequalities.
Key Words. Mixed variationallike inequality problems, iterative
schemes, cocoercive maps, strongly convex functions.
1. Introduction
Let H be a real Hilbert space whose inner product and norm are
denoted by ·, · and · , respectively. Let K be a nonempty convex subset
of H. Let T, A: KH and : KBKH be maps, and let f: K be a real
valued function. We consider the mixed variationallike inequality problem
