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Equilibrium Problems and Their Applications

Thesis Info

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Author

Zainab, Saira

Supervisor

Muhammad Aslam Noor

Program

PhD

Institute

COMSATS University Islamabad

City

Islamabad

Province

Islamabad.

Country

Pakistan

Thesis Completing Year

2011

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/handle/123456789/1851

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676726087556

Similar


The abstract theory of equilibrium problems has found its applications in various branches of nonlinear sciences. It provides us a unified structure to study an extensive number of linear and nonlinear physical problems. Since the projection method cannot be used to solve equilibrium problems, so we use auxiliary principle technique to solve equilibrium problems. Our main focus is to apply this technique to suggest several iterative algorithms (implicit and explicit) for solving different classes of equilibrium problems and their variant forms. Some other algorithms are suggested using the combination of auxiliary principle technique and so-called Bregman function. We also study the convergence analysis of these methods. We also consider and analyze a class of regularized mixed quasi variational inequalities. The auxiliary principle technique is again used to suggest some new iterative methods for solving the mixed quasi variational inequalities involving the skew symmetric bifunction. The convergence criterion of these iterative methods for solving the mixed quasi variational inequalities is considered under suitable conditions. Several special cases of these problems are considered. Results proved in this thesis continue to hold for known and new classes of equilibrium problems.
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ڈاکٹر عبدالحق

ڈاکٹر عبدالحق
ادھر عرصہ سے کوئی مہینہ خالی نہیں جاتا جب سینہ ملت کو کوئی نہ کوئی تازہ داغ نہ اٹھانا پڑتا ہو۔ ابھی مولانا مدنی اور مولانا ابوالکلام کا غم تازہ تھا کہ افضل العلماء مولانا ڈاکٹر عبدالحق صاحب نے داعی اجل کو لبیک کہا، وہ مدراس کے تھے، اس لیے شمالی ہند کے خواص کے علاوہ عام لوگ کم ان سے واقف تھے، وہ اپنے اوصاف و کمالات کے اعتبار سے بہت بڑی شخصیت رکھتے تھے اور آج مسلمانوں میں جیسے مرد مومن کی ضرورت ہے اس کا نمونہ تھے، ان میں علم و عمل کے سارے کمالات جمع تھے، دینی علوم کے بھی باضابطہ عالم تھے اور علوم جدیدہ کے بھی فاضل تھے، انھوں نے عربی کی تکمیل کے بعد انگریزی پڑھی اور آکسفورڈ سے ڈاکٹریٹ کی ڈگری حاصل کی، اس علم و فضل کے ساتھ بڑے دیندار اور عملی انسان تھے، انتظامی قابلیت بھی ان میں اعلیٰ درجہ کی تھی، مدراس کے مسلمانوں کی انھوں نے بڑی خدمت کی، تنہا اپنی کوشش سے مسلمانوں کے کئی ڈگری کالج قائم کیے اور وہ بجاطور پر مدراس کے سرسید کہلاتے تھے، مختلف اوقات میں بڑے بڑے تعلیمی عہدوں پر ممتاز رہے۔
اب سے چند سال پیشتر مسلم یونیورسٹی کے پرو وائس چانسلر بھی رہے تھے، اور اپنی قابلیت، دینداری اور حسن انتظام سے یونیورسٹی کی فضا بدل دی تھی، مگر اس سیکولر دور میں پھر مسلم یونیورسٹی جیسے مسلم ادارہ میں اس کی گنجائش کہاں، اس لیے تھوڑے ہی دنوں کے بعد مدراس پبلک سروس کمیشن کے ممبر بنادیئے گئے، اس وقت اس کے چیرمین تھے، مگر ان کی قابلیت اور تعلیمی تجربات کی بناء پر ممبر کی حیثیت سے یونیورسٹی کی مختلف تعلیمی اور انتظامی کمیٹیوں سے برابر ان کا تعلق قائم رہا اور وہ اس سے عملی دلچسپی لیتے رہے، حقیقۃً وہ...

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Incorporation of Social and Morel Values Through Secondary School Curriculum: A Content Analysis

This study was conducted to explore incorporation of social and moral values through the secondary school curriculum in Khyber Pakhtunkhwa, Pakistan. The study revolved around the following research questions: What are the social and moral values included in the secondary school textbooks? What are the important social and moral values missing in the secondary school textbooks? What are the benefits of inclusion of social and moral values in the textbooks at secondary school level? Data were collected from two sources: Secondary school textbooks and Secondary School Teachers. Four textbooks of the compulsory subjects (Urdu, Pakistan Studies, English and Islamiat) of the secondary classes and Secondary School Teachers of district Mansehra who taught compulsory subjects comprised the population of the study. The sample of the study consisted of twenty four lessons from the textbooks and twelve Secondary School Teachers. To collect data about social and moral values from Secondary School Teachers semi-structured interviews were used. Textbooks of secondary classes and transcribed interviews of twelve secondary school teachers were examined in the light of the operational definitions of social and moral values by applying qualitative content analysis technique. The entire data were coded and categories were formed from the codes. Codes were grouped into categories: social and moral values. Peer/expert debriefing was used to review and assess the data to enhance the validity and reliability of the analysis process and findings. The findings of the study revealed that the secondary school textbooks contained social values like equality, human rights, service of humanity, regard for one‟s family, dignity of labour and charity. The textbooks also contained moral values like truth, honesty, obedience, faith and sacrifice. Social and moral values were associated with human behaviour on the xvi basis of which good or bad behaviour of individuals and their adjustment in a society can be judged. Some important social and moral values, however, seemed lacking in the books. These include values such as responsibility, hard work, obedience to the law, unity, patriotism and universal brotherhood and moral values such as virtue, good manners, submission, moderation and patience. The study, therefore, recommends that these values may be incorporated in the secondary school textbooks for a more wholesome education and character development of the students.