اسلامی اور مغربی تناظر میں آزادی اظہار رائے کا تقابلی جائزہ

Freedom of Expression: A Comparative Study from Islamic & Western Perspective Living on the earth is all about freedom and as we know that the first man on the earth Adam was sent on the earth with the freedom to worship only to Allah. This freedom is a blessing of Allah and the value of it would only be judged in the era of slavery. It is an ultimate principle in Islam that the total submission is to be Allah alone. Thus, a man would never be a slave of any other person and whenever they become a slave to any other authority they are treated inhumanly. Allah (SW) made this glorious world for human beings and granted them the status of Ashraf ul Makhlūq. Human has such value which can be testified by this reason that everything is tightened to them and the world is only created for them. But human can only be benefited from the world till they are better for them and others, living friendly and create atmosphere of peace. So, till the end they will be benefited and blessed. They will also be in peace and freedom if they take care and have the respect for humanity. As man is a social animal and doesn’t live without his community. Sometimes due to controversy in thinking and other routes fall in conflicts, for which a proper law is administered. The differences in views are not forbidden. It is important, not to cross limits and to create peaceful atmosphere in order to rest humanity in peace and make the world peaceful. This article deals with the comparison of Islamic freedom of expression and the modern Western criterion of freedom of speech. The study concludes that the Islamic and western thought on freedom is different from each other.  In this study comparative and critical approach is adopted.

On Means and Inequalities for C0-Semigroup of Operators

The strongly continuous semigroups of operators are of great significance due to the fact that these have numerous applications in various areas of science. The qualitative understanding of a complicated deterministic system can be acquired by analyzing the solutions of a related differential equations in terms of these operators. Moreover, the theory of convexity, means, Cauchy means and inequalities has a huge impact in everyday science. Therefore, the pronounced nature of the means and inequalities defined on semigroups of operators, can not be contradicted. This dissertation is a staunch effort to generalize the theory of means and inequalities to the operator semigroups. A new theory of power means is introduced on a C0-group of continuous linear operators. A mean value theorem is proved. Moreover, the Cauchy-type power means on a C0-group of continuous linear operators, are obtained systematically. A Jessen’s type inequality for normalized positive C0-semigroups is obtained. An adjoint of Jessen’s type inequality has also been derived for the corresponding adjoint semigroup, which does not give the analogous results but the behavior is still interesting. Moreover, it is followed by some results regarding exponential convexity of complex structures involving operators from a semigroup. Few applications of Jessen’s type inequality are also presented, yielding the Hölder’s type and Minkowski’s type inequalities for corresponding semigroup. Moreover, a Dresher’s type inequality for two-parameter family of means, is also proved. A Jensen’s and Hermite-Hadamard’s type inequalities are also obtained for a semigroup of positive linear operators and a superquadratic mapping defined on a Banach lattice algebra. The corresponding mean value theorems conduct us to find a new sets of Cauchy’s type means.