Search or add a thesis

Advanced Search (Beta)
Home > Generalization of Mixed Means and Related Results

Generalization of Mixed Means and Related Results

Thesis Info

Access Option

External Link

Author

Khan, Khuram Ali

Supervisor

Josip Pecaric

Program

PhD

Institute

Government College University

City

Lahore

Province

Punjab

Country

Pakistan

Thesis Completing Year

2008

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/bitstream/123456789/2051/1/1718S.pdf

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676726257502

Similar


Inequalities lie at the heart of a great deal of mathematics. G. H. Hardy reported Harald Bohr as saying ‘all analysts spend half their time hunting through the literature for inequalities which they want to use but cannot prove’. Inequalities involving means open many doors for analysts e.g generalization of mixed means fallouts the refinements to the important inequalities of Holder and Minkowski. The well known Jensen’s inequality asserts a remarkable relation among the mean and the mean of function values and any improvement or refinements of Jensen’s inequality is a source to enrichment of monotone property of mixed means. our aim is to utilize all known refinements of Jensen’s inequality to give the re- finements of inequality among the power means by newly defined mixed symmetric means. In this context, our results not only ensures the generalization of classical but also speak about the most recent notions (e.g n-exponential convexity) of this era. In first chapter we start with few basic notions about means and convex functions. Then the classical Jensen’s inequality and the historical results about refinements of Jensen’s inequality are given from the literature together with their applications to the mixed symmetric means. In second chapter we consider recent refinements of Jensen’s inequality to refine inequality between power means by mixed symmetric means with positive weights under more comprehensive settings of index set. A new refinement of the classical Jensen’s inequality is also established. The Popovicui type inequality is generalized using green function. Using these refinements we define various versions of linear functionals that are positive on convex functions. This step ultimately leads us to viiviii the important and recently revitalized area of exponential convexity. Mean value theorems are proved for these functionals. Some non-trivial examples of exponential convexity and some classes of Cauchy means are given. These examples are further used to show monotonicity in defining parameters of constructed Cauchy means. In third chapter we develop the refinements of discrete Jensen’s inequality for con- vex functions of several variables which causes the generalizations of Beck’s results. The consequences of Beck’s results are given in more general settings. We also gen- eralize the inequalities of H ̈older and Minkowski by using the Quasiarithmetic mean function. In forth chapter we investigate the class of self-adjoint operators defined on a Hilbert space, whose spectra are contained in an interval. We extend several re- finements of the discrete Jensen’s inequality for convex functions to operator convex functions. The mixed symmetric operator means are defined for a subclass of positive self-adjoint operators to give the refinements of inequality between power means of strictly positive operators. In last chapter, some new refinements are given for Jensen’s type inequalities in- volving the determinants of positive definite matrices. Bellman-Bergstrom-Fan func- tionals are considered. These functionals are not only concave, but superlinear which is a stronger condition. The results take advantage of this property.
Loading...

Similar Thesis

Showing 1 to 20 of 100 entries
TitleAuthorSupervisorDegreeInstitute
PhD
Government College University, Lahore, Pakistan
PhD
Government College University, Lahore, Pakistan
PhD
Government College University, Lahore, Pakistan
PhD
Government College, Lahore, Pakistan
PhD
University of Peshawar, Peshawar, Pakistan
PhD
Government College University, Lahore, Pakistan
PhD
Government College University, Lahore, Pakistan
MA
Quaid-i-Azam University, Islamabad, Pakistan
Mphil
Riphah International University, Faisalabad, Pakistan
Mphil
Quaid-i-Azam University, Islamabad, Pakistan
PhD
University of the Punjab, Lahore, Pakistan
Mphil
Quaid-i-Azam University, Islamabad, Pakistan
Mphil
Quaid-i-Azam University, Islamabad, Pakistan
PhD
Quaid-I-Azam University, Islamabad, Pakistan
PhD
Government College University, Lahore, Pakistan
Riphah International University, Faisalabad, Pakistan
PhD
Government College University, Lahore, Pakistan
PhD
Government College University, Lahore, Pakistan
Mphil
Quaid-i-Azam University, Islamabad, Pakistan
MS
International Islamic University, Islamabad, Pakistan
TitleAuthorSupervisorDegreeInstitute
Showing 1 to 20 of 100 entries

Similar Books

Loading...

Similar Chapters

Loading...

Similar News

Loading...

Similar Articles

Loading...

Similar Article Headings

Loading...

ڈاکٹر صابر کلوروی

ڈاکٹر صابر کلوروی مرحوم
شبلی ڈگری کالج اعظم گڑھ کے علامہ شبلی سمینار میں پاکستان کا ایک وفد جناب ریاض مجید کی قیادت میں آیا تھا، ڈاکٹر عبدالعزیز ساحر اور محترمہ رابعہ سرفراز کے ساتھ ایک شخصیت ڈاکٹر صابر کلوروی کی تھی، متین، کم سخن لیکن کشش کے مالک، شبلی کی تنقید نگاری کے عنوان سے ان کے مقالے نے بڑی داد حاصل کی۔
دو دن کے مختصر قیام کے بعد جب وہ اور ان کے رفقا رخصت ہوئے تو رخصت کرنے والوں نے کہا کہ سرحد پار سے آنے والے اس دستۂ علم نے ایک بار پھر دلوں کو فتح کرلیا، علامہ شبلی اور ان کی یادگاروں خصوصاً دارالمصنفین سے ان کی غیر معمولی محبت کسی عقیدت مند زائر کے جوش و شوق کی عکاس تھی، وہ بادیدۂ نم رخصت ہوئے تھے اور کسے خبر تھی کہ اتنی جلد وہ اس دنیا سے ہمیشہ کے لیے رخصت ہوکر بے شمار پلکوں کو نم کرجائیں گے، ان کے انتقال کی خبر موقر رسالہ ’’اخبار اردو‘‘ اسلام آباد سے ملی، ۳۱؍ اگست ۱۹۵۰؁ء سے شروع ہوکر ۲۲؍ مارچ ۲۰۰۸؁ء کو ختم ہونے والا یہ سفر مختصر ہی کیا جائے گا لیکن کلوروی مرحوم نے اپنی صفت و لیاقت سے اس قلیل مدت کو پرثروت بنادیا، اقبالیات ان کی ادبی کاوشوں کا سر عنوان ہے، ’’یاد اقبال، داستان اقبال، اشاریہ مکاتیب اقبال، اقبال کے ہم نشین، تاریخ تصوف‘‘، کتابوں کے علاوہ ان کا اصل کارنامہ ان کی تھیسس ’’باقیات شعر اقبال‘‘ ہے ڈاکٹر عطش درانی اور دوسرے اہل قلم کی تحریروں سے اردو لسانیات میں ان کی منفرد اور امتیازی خوبیوں کا علم ہوا، مشفق خواجہ نے ان کو غریق تحقیق کہا تھا، اﷲ تعالیٰ غریق رحمت کرے، معارف، پشاور یونیورسٹی میں ان کے کسی رفیق یا شاگرد سے ان کے متعلق ایک مفصل مضمون کی توقع کرسکتا ہے۔

مروّجہ انعامی اسکیمیں اور ان کی شرعی حیثیت

Islam is a complete code of life. It provides injunctions for every field of life. In economics it not only provides us details in finance and trade but also provides us information about "Halal & Haram". Needless to emphasize that economy plays an important role in the development of nation and financial matters cannot be ignored if development is a target. According to Islamic teachings all earnings must be lawful. Generally, new ways are being adopted to increase and generate wealth. Islam encourages to get more wealth and profit but no illegal means should be adopted for that. All kinds of fraud and unfair means while doing business must be avoided. Islam lays stress on using lawful and valid means in all economic activities. Scholars of Sub-continent have different opinions about the prevailing prize money schemes. Some scholars consider them lawful regarding some aspects but majority term them unlawful.

Studies on Indigenous Plants of Karachi for the Control of Root Rot-Root Knot Disease Complex

Several indigenous plants in Karachi region possessed various antimicrobial properties, among them some plants viz., Cyamopsis tetragonoloba (L.) Taub, Fagonia indica Burm f., Hibiscus rosa-sinensis L., Melia azedarach L., Prosopis juliflora (Sw.) DC., Rhynchosia minima (L.) DC., Solanum surattense Burm f., Terminalia catappa L., Thespesia populnea (L.) Sol. ex Corrêa, Withania somnifera (L.) Dunal were selected for present study. These plants were collected from different localities of Karachi and their grinded powders were used in vitro and in vivo against soil-borne plant pathogens like root-rot fungi and root-knot nematode. In vitro different parts of selected plants were extracted in five solvents such as water, methanol, n-hexane, chloroform and ethyl acetate. These extracts were tested against three root-rot fungi viz., Fusarium oxysporum Schltdl. emend. Snyd. & Hans., Macrophomina phaseolina (Tassi) Goid and Rhizoctonia solani (Kühn) by food-poisoned method on potato dextrose agar medium. Leaves, fruit and shoot extracts of selected plants significantly suppressed the growth of fungi as compared to stem extracts. However, H. rosa-sinensis (stem) extracts showed fungicidal activity than its leaves extracts. Among solvents, the water and methanol were found more effective against almost three fungi. Plants extracts were also tested against eggs hatching and mortality of second stage juveniles (J2) of root-knot nematode (Meloidogyne javanica (Treub) Chitwood) with varying concentrations (10, 5 and 2.5%). Significant reduction in the eggs hatching and increased in mortality was noticed in all plant extracts. Eggs hatching have been reduced and larval mortality has been increased when concentration of extracts increased therefore concentration 10% showed maximum nematicidal activity. Screen house trials were conducted in department of Botany, Federal Urdu University, to assess in vivo potential of plant species against targeted fungi and nematodes. Experiments carried out on okra (Abelmoschus esculentus (L.) Moench), mung bean (Vigna radiata (L.) R. Wilczek), cowpea (Vigna unguiculata (L.) Walp) and chickpea (Cicer arietinum L.). In soil amendment (organic amendment) experiment powder of plants were mixed in soil @ 0.5, 1 and 2% w/w fifteen days prior before sowing the seeds. T. populnea (leaves), M. azedarach (leaves), W. somnifera (leaves & stem), T. catappa xiii (leaves), P. juliflora (leaves), H. rosa-sinensis (stem), S. surattense (shoots) and C. tetragonoloba @ 1 and 2% showed more significant results than other plants. Amendment not only suppressed the incidence of root rot-root knot disease complex but it also enhanced the growth of test crops (okra & mung bean). Biochemical estimation of okra and mung bean also has been done after uprooting the crops. It was observed that T. populnea (leaves), M. azedarach (leaves) and W. somnifera (leaves) highly enhanced chlorophyll “a”, “b”, carotenoids and carbohydrate as compare to other treatments and control in okra. However, in mung bean S. surattense (shoots), H. rosa-sinensis (stem) and P. juliflora (leaves) highly enhanced the physiological parameters. Water extracts @ 1 and 2% w/v of selected plants has been used as soil drenching to check their efficacy. Both concentrations significantly promote growth of cowpea plant and also suppressed the infection caused by root-rot fungi and root-knot nematodes. However, W. somnifera (leaves) and S. surattense (shoots) extracts showed highly significant results as compared to others. The biochemical contents of cowpea showed increase in chlorophyll “a”, “b”, carotenoids, carbohydrate and decrease in phenol content. Combined application of microbial antagonists (Trichoderma harzianum & Pseudomonas aeruginosa), nematicide (Carbofuran) and fungicide (Aliette) in soil amended with plants dry powder @ 1 and 2% w/w showed remarkable suppression of root rot-root knot disease complex. While W. somnifera (leaves), S. surattense (shoots) and H. rosa-sinensis (stem) adequately affected on growth parameters of chickpea and reduced infection of targeted pathogens. On the other hand combination of plants powder (W. somnifera and S. surattense, H. rosa-sinensis and T. populnea) with P. aeruginosa, T. harzianum, Aliette and Carbofuran significantly enhanced biochemicals than other treatments.