Investigation of the relationship between equilibrium and fixed point and data dependence

Since fixed point theory is an interdisciplinary theory, it is related to equilibrium problems, which is one of the main topics of economics. Fixed point theory is used to calculate, analyze and formulate solutions to economic equilibrium problems. Equilibrium problems have entered the literature as generalizations of optimization and variational inequalities. It has been studied by many authors in different structures. Among them is the viscosity approximation method. In this thesis, using the viscosity approximation method, a new iteration method is introduced to find a common element of the set of fixed point of a class of relaxed (a,b)- cocoersive mapping and nonexpansive mapping in Hilbert space, the solution set of an equilibrium problem and the solution set of a variational inequality.It is proved that this iteration method converges strongly to a common element of the above three sets under some conditions. An application supporting the convergence theory is also given. Finally, the concept of data dependency is examined using the defined iteration method for solving the equilibrium problem.