Auxiliary Principle and Iterative Algorithms for Completely Generalized Mixed Implicit Equilibrium-Like Problems in Banach Spaces
Guangqiang Xiao · Acta Analysis Functionalis Applicata · 2008
A new class of completely generalized mixed implicit equilibrium-like problems (CGMIELP)which do not contain inner product but replaced by a bilinear continuous function F is introduced in Banach space.Then,a concept called F-strongly monotonicity is defined.Next,a generalized auxiliary problem is suggested to study this class of equilibrium problem and the existence theorems of the solution of the generalized auxiliary problem is also proved.Finally,a novel and innovative iterative algorithm is given and the convergence criteria of iterative sequences generated by the algorithm is shown.