تمسکات میں سرمایہ کاری اور اس کی شرعی حیثیت تحقیقی وتجزیاتی مطالعہ

Islam is a complete code of life which provides guidance in political, social and economic affairs. Economics deals with very importnt sphere of human life that involves struggle for survival. This struggle is always appreciated because Allah Almighty Himself motivates for it. The basic aim of this is to eradicate poverty and huger and to bring happiness and satisfaction in society but the condition is that all the economic activities should be done with within the limits of sharia. Otherwise the efforts of human beings in this world as well as hereafter will never be successful. In contemporary economic trends, investment in securities is well known and popular. Government and private institutions issue bonds, shares, debentures etc to provide economic security to the people but in various types of sceurities Shar฀‘ah laws are not taken care of. Where, for a Muslim, injunctions of Shar฀‘ah are everything. There are tidings of rewards on obeying these injunctions and warning of punishment on their violation boath in this world and hereafter. Economic experts suggest to invest but People remain uncertain in these schemes. Regarding this objective, in this article few types of securities (Shares, Debentures and Prize Bonds) have been discussed in Shar฀‘ah perspectives and prize bonds were given special attention because of difference of openion of scholars about it. Some alternate solutions which may provide an insight into Islamic fiscal monetary system have been provided at the end.

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.