Summary: JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS: Vol. 108, No. 3, pp. 527541, MARCH 2001
Iterative Schemes for Solving Mixed
Q. H. ANSARI
AND J. C. YAO
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 variational-like inequalities. We use the
concept of -cocoercivity to prove the convergence of the approximate
solutions to the exact solution of mixed variational-like inequalities.
Key Words. Mixed variational-like inequality problems, iterative
schemes, -cocoercive maps, -strongly convex functions.
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 variational-like inequality problem