Fixed Point Theorem For Weakly Contractive Multi-valued Mapping And Generalized Equilibrium Problem

The problem of existence of fixed point theorems for multi-valued maps which satisfy weakly contractive conditions and the problem of a generalized equilibrium in Hilbert spaces are discussed in this paper, the paper contains three parts as following:In charter one, the background of title, main contents that we will discuss and significance are introduced.In charter two, the conception of weakly contractive multi-valued mapping is introduced in the partially ordered complete metric space, and some new (coupled) fixed point theorems for weakly contractive multi-valued maps are proved.In charter three, an iterative scheme about a multi-valued non-expansive map-ping and a generalized equilibrium problem is constructed in Hilbert spaces, and strong convergence of the scheme to common element of the two sets is proved. The conclusions of this paper extend and improve the relevant results of some references.