Global Structural Changes and Global Islamic Identity

Globalization is slowly changing life and traditions of many people over the World, dramatically seeking changes in the traditional relationship between the community and people, creating a new sensibility and creativity in relationships between social groups. These changes necessarily require a new social and political model of organization for community, reorganizing and changing the nature of relationship between states.  Effort to protect identity of people usually convey in the form of the fear of the subservient economic, cultural and political position in the process of globalization. This fear frequently produces powerful vibrations indicating the need of integration of social groups with the same or similar cultural identity, what opens up a new dimension of the internal political crisis between government and society. This crisis will produce particularly dramatic changes in Islamic world generating a powerful conflict between state and society in Islamic world, with unpredictable development of relations between Islam and West.

On a Class of Variational Inequalities

A novel generalization of variational inequalities, which is called strongly mixed variational inequalities, is introduced and investigated. It is shown that the minimum of a sum of differentiable convex functions and nondifferentiable strongly convex functions can be characterized by strongly mixed variational inequalities. Auxiliary principle technique is used to investigate the existence of the unique solution of strongly mixed variational inequalities. This technique suggests us to propose some iterative schemes for solving strongly mixed variational inequalities. It is shown that strongly mixed variational inequalities are equivalent to fixed point problem and the resolvent equations under some conditions. These equivalent formulations can be used to examine the existence of a solution of the strongly mixed variational inequalities as well as used to develop new iterative schemes for solving strongly mixed variational inequalities. Convergence criteria of proposed methods is analyzed under some conditions. Dynamical systems related to strongly mixed variational inequalities is introduced. This approach is also used to examine the existence of the solution of strongly mixed variational inequalities. The error bounds for a solution of the strongly mixed variational inequalities using the merit function technique are derived. Moreover various special cases have also been discussed. System of strongly mixed variational inequalities involving two different operators is considered.