Study On Iterative Algorithm About The Equilibrium Problem And Common Fixed Point Problem

Fixed point theory of nonlinear operator is an important part of nonlinearfunctional analysis, the fixed point existence and iterative convergence problem ofnonlinear operator has become a active topic of research of nonlinear functionalanalysis in recent years. In this article, the author mainly study on iterativeconvergence problem of operator, a new iterative algorithms citation to approach acommon element of generalized mixed equilibrium problem, variational inequalityproblem, and the set of operator fixed point, the results improve and extend thecorresponding results in some references. The full text is divided into three chapters:The first chapter: introduces the background of iterative algorithm about theory ofnonlinear operator and related concept and mark and definition and the paper’s mainwork.The second chapter: discusses the strong convergence theorem of generalizedmixed equilibrium problem and fixed point problem of non-expansive mappings inHilbert space.The third chapter: discusses the iterative algorithm with infinite equilibriumproblem and fixed point problem of non-expansive mappings in Hilbert space.