میں اور تو
ہماری زندگی ہے کچھ یوں منتشر
جیسے دو متوازی خطوط کا سفر
نہ ابتدا میں لچک
نہ انتہا پہ خم
بس محو ِ سفر ہیں
نہ ابتدائے سفر کا جنوں
نہ وصال منزل کی لذت
فقط اک خلا ہے
جو درمیاں پڑا اونگھ رہا ہے
یہ ’’تُو‘‘،’’میں‘‘کے دو خطوط
Islam covers all aspects of human life. It is not only a religion but also a complete code of life. Hazrat Muḥammad ﷺ is the last Rasool of Allah Almighty. All his life is a translation and interpretation of the Holly Qur’ān. In this article, it is proved that the fundamental rules of Islamic foreign affairs are the torchbearer and leader for the modern age world. If we make a deep study of Christianity, Judaism, Hinduism or any other religion or school of thought of the world we would not find a complete and permanent solution related to peace, security and prosperity in the world. Islam gives us the golden rules for one person, society or state in the field of making relations with others individually and collectively. Islam lays great stress on equality, social justice, brotherhood and peace not only in the state but across the border too. The fundamental rules of Islamic foreign policy not only emphasize the faith in the oneness of Allah but also the equality among all human beings and all races and nations. Islam builds international relations on a humanitarian base.
In almost everyeld of science, inequalities play an important role. Although it is very vast discipline but our focus is mainly on Ostrowski type inequalities. Our aim is to discuss some weighted and non-weighted Ostrowski type inequalities with parameters and related results including Gr uss,Ceby sev and Ostrowski-Gr uss inequalities along with applications. Firstly, we generalize Ostrowski inequality for di erentiable functions in three di erent cases, that are bounded functions, bounded below functions and bounded above functions. Secondly, we introduce generalized inequalities of Ostrowski type for mappings on Lp spaces and of bounded variation. A weighted Ostrowski type inequality for twice di erentiable functions with bounded second derivatives and absolutely continuousrst derivatives are also discussed. Moreover, we generalize weighted Ostrowski-Gr uss type inequality with parameter for di erentiable functions by using weighted Korkine''s identity. Furthermore, we provide generalizations of Ostrowski type integral inequality with bounded derivatives by using the Riemann-Liouville fractional integral. We would like to give some generalizations of Ostrowski type inequality with better bounds. In addition, we modifyCeby sev inequality for two independent variables involving parameters. In the process of generalizing the Ostrowski type and its associated inequalities, we achieve new Montgomery identities with parameters for fractional, weighted and second order di erentiable functions of two variables. We will also discuss applications of our results in probability density function and numerical quadrature rules fornding error bounds of midpoint, trapezoidal, 1 3 Simpson''s, 3 8 Simpson''s and some non-standard quadrature rules. Our dissertation retrieves many established results. At places we will also obtain better bounds of di erent inequalities.