تمهيد

حياة نسيم حجازي ومكانته العلمية والأدبية في الأدب الأردي

Abstract: The article deals with the life and contribution ofNaseem Hijazi towards reconstruction ofIslamic thought through his historical novels in New Muslim generation. As a novel writer < Naseem Hijazi is regarded as one of thefinest writers of Urdu language especially in the later 20th century. Among his popular contemporaries were Ibn-e-Safh Saadat Hasan Manto< and Shqfiq-ur-Rehman< all having their particular line ofliterature. Naseem Hijazi is knownfor his potent and romantic description of history. There are only two writers prior to Hijazi who wrote history novels in Urdu: Abdul Haleem Sharar and Sadiq sardhunwi < but Hijazi’s writing is most credible in terms of historical description and accuracy. He exercised extra care to back his study of history by through research and to cite his sources whenever possible. Hijazi creates his powerful expression by blending this study of history with fairytale romanticism. The story usually revolves around characters who were related to< and shown present at the actual historical event that wishes tofocus on. Naseem Hijazi bases most ofhis work in Islamic history. In dealing with this history' he shows both the rise and fall of the Islamic Empire. This writer seems to have been inspired a lot by Allama Muhammad Iqbal's poetry. He tries, not very unlike Iqbal, to remind his readers of the lost glory of the Muslims and in a way inspire them to work with commitment to achieve lost glory in all walks of life. Naseem Hijazi has immensely influenced his readers both in and out of Pakistan. He has been one of the key sources of Islamist ideologies in Pakistan and worked as a key ideology and valour builder during the Soviet-Afghan War. Many Pakistani educated Youngsters throughout 1950s till today are believed to have been emotionally and ideologically inspired by his writings. He enjoys a very large reader base even after his death.

Inequalities Involving Starshaped and Related Functions

Inequalities play an important role in almost all branches of mathematics as well as in other areas of science. Books by Hardy, Littlewood and P ́lya appeared in 1934 o [50], Beckenbach and Bellman published in 1961 [27] and by Mitrinovi ́ published c in 1970 [59] made significant contributions to the field of inequalities and provides motivations, ideas, techniques and applications. Since 1934 a huge amount of effort has been devoted to the discovery of new types of inequalities and to the applications of inequalities in many parts of analysis. The usefulness of mathematical inequali- ties is felt from the very beginning and is now widely acknowledged as one of the major driving forces behind the development of modern real analysis. The theory of inequalities is in a process of continuous development state and inequalities have become very effective and powerful tools for studying a wide range of problems in var- ious branches of mathematics. This theory in recent years has attracted the attention of a large number of researchers, stimulated new research directions and influenced various aspects of mathematical analysis and applications. Among the many types of inequalities, those associated with the names of Jensen, Hadamard, Hilbert, Hardy, Opial, Poincare, Sobolev, Levin and Lyapunov have deep roots and made a great impact on various branches of mathematics. The last few decades have witnessed important advances related to these inequalities that remain active areas of research and have grown into substantial fields of research with many important applications. The present monograph provides a systematic study of some of the most famous and fundamental inequalities. There is no doubt that convex functions play an im- portant role in the theory of inequalities. Many important inequalities are the con- sequences of the applications of convex functions. For example Jensen’s inequality Hadamard’s inequality for convex functions provided a good start in the development of the theory of inequalities. Some other important classes of functions are based on the definition of convex functions. Sometime it turns out to be more convenient to replace convex function with starshaped function. A convex function passing through the origin is starshaped. It is very interesting to note that now Jensen’s, Hadamard’s and many other inequalities have their generalizations, refinements, improvements by using as tool a class of functions which are more than convex functions. This is class of superquadratic functions introduced by S. Abramovich, G. Jameson and G. Sinnamon. In the first Chapter we give basic notions and results briefly to provide the moti- vation and make the monograph friendly readable. In Chapter 2 we give refinements of the inequalities of Acz ́l, Popoviciu and Bell- e man and some results related to power sums. We also consider divergence measures, J-divergence, K-divergence and results related to these measures are proved. In Chapter 3 we give results related to Hadamard’s and Jensen’s inequalities for superquadratic functions. Then we give generalizations and improvements of these results by using converse Jensen’s inequality for superquadratic functions. Also we consider refinement of Hardy’s inequality and prove analogue results. In the last Chapter we consider an Opial type integral inequality for a particu- lar class of convex functions. We prepare results to give applications to fractional derivatives.