Abstract:
The abstract theory of equilibrium problems has found its applications in various
branches of nonlinear sciences. It provides us a unified structure to study an extensive
number of linear and nonlinear physical problems. Since the projection method cannot be
used to solve equilibrium problems, so we use auxiliary principle technique to solve
equilibrium problems.
Our main focus is to apply this technique to suggest several iterative algorithms (implicit
and explicit) for solving different classes of equilibrium problems and their variant forms.
Some other algorithms are suggested using the combination of auxiliary principle
technique and so-called Bregman function. We also study the convergence analysis of
these methods. We also consider and analyze a class of regularized mixed quasi
variational inequalities. The auxiliary principle technique is again used to suggest some
new iterative methods for solving the mixed quasi variational inequalities involving the
skew symmetric bifunction. The convergence criterion of these iterative methods for
solving the mixed quasi variational inequalities is considered under suitable conditions.
Several special cases of these problems are considered. Results proved in this thesis
continue to hold for known and new classes of equilibrium problems.
