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General Inequalities for Generalized Convex Functions

Thesis Info

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External Link

Author

Khan, Asif Raza

Supervisor

Josip Pecaric

Program

PhD

Institute

Government College University

City

Lahore

Province

Punjab

Country

Pakistan

Thesis Completing Year

2012

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/bitstream/123456789/2538/1/2583S.pdf

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676726256853

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It is a fact that, the theory of inequalities, priding on a history of more than two cen- turies, plays a significant role in almost all fields of mathematics and in major areas of science. In the present dissertation, we will study the general inequalities, namely integral inequalities and discrete inequalities for generalized convex functions. There- fore, we will introduce some generalized convex functions which include functions −convex functions, and n−convex func- with nondecreasing increments, ∆− and tions of higher orders. By using these functions, we will provide a generalization of the Brunk’s theorem, of the Levinson-type inequalities, of the Burkill-Mirsky-Peˇari ́’s re- c c sult and of the result related to arithmetic integral mean. We will also discuss the Popoviciu-type characterization of positivity of sums and integrals for higher order convex functions of n variables and we will give some related results. Our disserta- tion also provides generalizations of some of the celebrated and fundamental identities ˇ and inequalities including Montgomery’s identities, Ostrowski-, Gr ̈ss-, Cebyˇev- and u s Fan-type inequalities. Moreover, we will also apply an elegant method of producing n−exponentially and logarithmically convex functions for positive linear function- als constructed with the help of majorization-type results, Favard-, Berwald- and Jensen-type inequalities. The generalization and the following refinements of Jensen- Mercer’s inequalities are also provided with some applications. The Lagrange- and Cauchy-type mean value theorems are also proved and shown to be useful in studying Stolarsky-type means defined for the positive linear functionals.
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91. Al-Shams/The Sun

I/We begin by the Blessed Name of Allah

The Immensely Merciful to all, The Infinitely Compassionate to everyone.

91:01
a. By the sunrise and its brightness,

91:02
a. and the moon as it follows it,

91:03
a. and the daylight as it displays its brightness,

91:04
a. and the nighttime as it covers it,

91:05
a. and the celestial realm and how HE built it,

91:06
a. and the earth and how HE spread it out,

91:07
a. and the soul and how HE formed it perfectly,

91:08
a. and inspired it - the soul - with its instincts of
- evil/vice - whatever will lead it away from the truth, and
- piety - whatever will keep it close to the truth.

91:09
a. Indeed, the one who purifies one’s soul of evil will succeed in the Sight of Allah,

91:10
a. and the one who corrupts one’s soul with evil will fail in the Sight of Allah.

91:11
a. The Tribe of Thamud denied and belied their Prophet Saleh
b. through their transgression.

Surah 91 * Ash-Shams 739

91:12
a. When the most wretched among them rushed forward -
b. to maim and savagely kill the she-camel.

91:13
a. And, the Messenger of Allah - Saleh - told them:
b. This is ‘the she-camel of Allah!’
c. Give her time to drink’ at the wells.

91:14
a. But they denied and belied him, and
b. maimed and savagely killed her.
c. So their...

البعثات التعليمية المغربية إلى الخارج؛ فشل أم إفشال

تسعى الدراسة لتسليط الضوء على موضوع البعثات التعليمية إلى الخارج، زمن السلطانين محمد الرابع والحسن الأول، والتي جاءت كرد فعل جراء الهزائم المتتالية التي تكبدها الجيش المغربي؛ (هزيمة إيسلي، هزيمة تطوان) وما ترتب عنها من وهن أصاب في العمق جميع الميادين: (عسكرية، اقتصادية، سياسية، اجتماعية..). مبرزين فيها أهم الأسباب التي كانت وراء إرسالها، والدول التي قصدتها من أجل التكوين العسكري على الخصوص. وفي الأخير حاولنا إبراز أهم العوامل التي كانت وراء فشلها وإفشالها؛ لكي لا تحقق الأهداف المسطرة لها، المتمثلة أساسا في بناء جيش بمواصفات حديثة قادر على حماية المغرب من الأطماع الخارجية. وفي سبيل ذلك استخدم الباحث المنهج التاريخي المقارن، وتوصلت الدراسة الى مجموعة من النتائج أهمها: أن المغرب لم يكن مهيئاً بما يكفي للاستفادة من عائدات هذه البعثات، إن على المستوى الرسمي أو الشعبي. وكان الفشل أولا، ثم الإفشال ثانيا أهم نتيجة توصلنا إلينا، وهذا ما سلطنا عليه الضوء في خاتمة هذه الدراسة.

Outcomes of Turco’S Procedure for Idiopathic Clubfoot Among Children at French Medical Institute for Mothers and Children from January 2011 to July 2016

Background: Clubfoot known as Congenital Talipes Equino Varus Deformity (CTEV) is one of the most common congenital foot deformities. Affect 1-2/1000 live births worldwide. Males are more affected with Club foot compared to female. Idiopathic clubfeet was considered 80% as isolated birth defects and 20% are syndromic or neurogenic. Objective: 1. To estimate the demographic characteristics of patients with clubfoot at FMIC, Kabul, Afghanistan from 2011 to July 2016. 2. To determine the outcomes of Turco’s Procedure for idiopathic clubfoot among children from 2011 to July 2016 at Paediatric Orthopaedic Department of FMIC, Kabul, Afghanistan.Methodology: A descriptive case series study design is used to determine the outcomes of Turco’s Procedure for idiopathic clubfoot among children at Paediatric Orthopaedic Department of French Medical Institute for Mothers and Children (FMIC), Kabul, Afghanistan during January 2011 to July 2016. Records of 99 participants with 151 feet who had undergone Turco’s procedure were clinically and radiologically assessed and followed for 3 years. Self-developed structured questionnaire was used by applying consecutive sampling technique. Age range of the study participants was from nine months to five years. The descriptive analysis was done, using SPSS Version 22. Mean and standard deviation (SD) were calculated for Quantitative continuous/discrete variables. Frequency and proportions were calculated for categorical variables. T- test for two independent samples and Chi-square test also were run for few variables.Result: Out of 99 participants, 67(67.7%) males and 32(32.3%) females were affected; males were affected twice as often as girls. 52 (52.5%) participants were bilaterally, 26 (26.3%) Right side and 21 (21.2%) were Left side affected. 25 (25.3%) participants had positive family history. Hospital length of stay at hospital was 1.7 days (1 to 7 days). Participant’s feet were assessed clinically and radiologically. The results showed that Turco’s procedure in 79.8% of participants was successful and 20.2% of them had developed some kinds of complications. Family satisfaction rate was 89% found in the study. Conclusion: Clubfoot is one of the most common congenital foot deformities and patients with idiopathic clubfoot can be successfully treated in most of the cases by Turco’s procedure; Outcome of the surgery will be better if patient gets treatment at appropriate age. Overall, an 80% success rate of Turco’s procedure was found in this study