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Hadamard-Type Inequalities With Applications

Thesis Info

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Author

Muhammad, Iqbal

Program

PhD

Institute

University of Engineering and Technology

City

Lahore

Province

Punjab

Country

Pakistan

Thesis Completing Year

2014

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/handle/123456789/1422

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676726355274

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The vii study presents some of the fundamental results annexed to the Hermite Hadamard inequality. It aims at improving the role of distinct classes of convexity in the theory of Inequalities. This dissertation is devoted to sift out several refinements, generalizations, improvements and extensions of the Hermite Hadamard type inequalities for functions whose absolute values of first and second derivatives belong to class of convex functions. Eventually, as applications, the obtained results are employed for special means of real numbers. Explicit bounds are also being derived to versatile composite quadrature rules in terms of variety of functions belonging to different classes of convex functions. The analysis sets aside the determination of the partition required that would ensure that the accuracy of the result would be within a prescribed error tolerance. This way, this thesis caters a study of some inequalities analogous to the most acclaimed and basic Hadamard inequality. The study piles up interesting developments in this research field under a unified framework. This work will be of keenness to mathematical analysts, pure and applied mathematicians, physicists, engineers, computer scientists and other areas of science.
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سری پرکاش جی

سری پرکاش جی
افسوس ہے کہ گذشتہ مہینہ ہندوستان کی دو نامور شخصیتوں سری پرکاش جی اور پروفیسر محمد حبیب نے وفات پائی، سری پرکاش کی شخصیت مختلف حیثیتوں سے بڑی اہم تھی، وہ ہندوستان کے مشہور فلسفی صوفی ڈاکٹر بھگوان داس کے فرزند اور پنڈت جواہر لال نہرو کے پرانے معتمد علیہ رفیق تھے، انگلستان کی تعلیم کے زمانہ سے لے کر ہندوستان کی جنگ آزادی اور اس کے بعد تک ہر مرحلہ میں دونوں کا ساتھ رہا، آزادی کے بعد سری پرکاش حکومت کے ذمہ دار عہدوں پر رہے اور بڑی خوبی سے اپنے فرائض انجام دئیے اور اپنے اخلاص اور سلامت روی کی بنا پر پاکستان میں بھی ہائی کمشنری کے زمانہ میں مقبول رہے اور دونوں ملکوں کو قریب لانے کی کوشش کی، وہ ہماری پرانی مشترک تہذیب کی یادگار اور ہندو مسلم اتحاد کے بہت بڑے علمبردار تھے اور آخر تک اس پر قائم رہے، ان کا سب سے بڑا وصف ان کی بے تعصبی، فراخدلی اور اخلاقی بلندی تھی، وہ سیاست میں بھی صداقت و اخلاص پر عامل تھے، جو آجکل کے سیاسی لیڈروں میں کمیاب ہے اس لیے آزادی کے بعد کے حالات سے بہت بددل تھے، عرصے سے خانہ نشینی اختیار کرلی تھی، لیکن کبھی کبھی اپنے خیالات اخبار کے ذریعہ ظاہر کرتے رہتے تھے، ایک دو مرتبہ پنڈت جواہرلال نہرو کے ساتھ دارالمصنفین بھی آئے تھے، اور یہاں کے بزرگوں سے ان کے تعلقات تھے، وہ جس تہذیب کی پیداوار تھے اس کا دور اب ختم ہوگیا، سری پرکاش اس کی آخری یادگار تھے، اب ایسے نمونے نہ پیدا ہوں گے۔ (شاہ معین الدین ندوی، جولائی ۱۹۷۱ء)

 

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