علم اسباب ورود الحدیث: ایک تحقیقی جائزہ

Asbab-e-worood-e-Hadith means the context of background of a Haith. It is impossible to understand the original myth of hadith without knowing its background and context. This Article presents the concept of asbab-e-worood-e-Hadith. The discussion has been premeditated to explore the meanings and importance of asbab-e-worood. In this regard, keeping in view the nature of topic, the guidance has been sought from the Ahadith of Holy Prophet (PBUH). Asbab-e-worood in its nature having similarities with asbab-e-nazool-e-Quran. This article also describes the relationship between asbab-e-worood-e-hadith and asbab-e-nozool-e-Quran. In this regard some examples have been discussed also. This article also describes how asbab-e-worood is important to specify the meanings of text and explain the textual ambiguities. Key Words: Asbab-e-worood-e-Hadith Asbab-e-Nozool-e-Quran Sabab-e-worood qasasia 4.         Sabab-e-worood sawalia

Generalized Ostrowski Type Inequalities With Applications

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.