A general iterative method for two maximal monotone operators and 2-generalized hybrid mappings in Hilbert spaces

作者：Wangkeeree Rabian^*; Boonkong Uraiwan

来源：Fixed Point Theory and Applications, 2013, 2013(1): 246.

DOI：10.1186/1687-1812-2013-246

• 2-generalized hybrid mapping
• inverse strongly monotone mapping
• maximal monotone mapping
• hierarchical variational inequality

Let C be a closed and convex subset of a real Hilbert space H. Let T be a 2-generalized hybrid mapping of C into itself, let A be an alpha-inverse strongly-monotone mapping of C into H, and let B and F be maximal monotone operators on D(B) subset of C and D(F) subset of C respectively. The purpose of this paper is to introduce a general iterative scheme for finding a point of F(T) boolean AND (A + B)(-1) 0 boolean AND F-1 0 which is a unique solution of a hierarchical variational inequality, where F(T) is the set of fixed points of T, (A + B)(-1) 0 and F-1 0 are the sets of zero points of A + B and F, respectively. A strong convergence theorem is established under appropriate conditions imposed on the parameters. Further, we consider the problem for finding a common element of the set of solutions of a mathematical model related to mixed equilibrium problems and the set of fixed points of a 2-generalized hybrid mapping in a real Hilbert space.

• 出版日期2013-11-7