عصر حاضر میں بین المذاہب ہم آہنگی کی ضرورت و اہمیت

The enmity and differences among nations have risen along with the increasing distances among people. Therefore, the need of hour is to develop the spirit of harmony and understanding among the followers of revealed religions. The Messengers and Prophets were designated by Allah to promote and promulgate, justice, tolerance, love and harmony among His creations. Islam is a religion based on characteristics of peace, love, respect, tolerance, dignity and denial of extremism, which are in the contemporary world ideal for interaction among nations. Islam teaches to respect all the religions and prophets to maintain and sustain the peace and harmony. The advanced technology of modern world and inventions demand intense responsibility to maintain and enhance the better human relations in Political, Social, Economic, Religious, and Cultural spheres of life. The present article envisions all those dimensions, which are essential for interfaith harmony.

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.