1. UKM Learning and Research Repository
2. PHD Thesis / Tesis PHD
3. Faculty of Science and Technology / Fakulti Sains dan Teknologi

Title:	Several inequalitiesof Hermite- Hadamard, Ostrowski and Simpson type for s-convex, quasi-convex and r-convex mappings with some applications
Authors:	Mohammad Wajeeh Nawaf Alomari (P41880)
Supervisor:	Maslina Darus, Prof.Dr.
Keywords:	Inequalities (Mathematics) Functions special Universiti Kebangsaan Malaysia -- Dissertations Dissertations, Academic -- Malaysia
Issue Date:	28-Jan-2011
Description:	Inequalities play a significant role in almost all fields of mathematics. Several applications of inequalities are found in various areas of sciences such as, physical, natural and engineering sciences. In numerical analysis, inequalities play a main role in error estimations. A few years ago, a number of authors have considered an error analysis of some quadrature rules of Newton-Cotes type. In particular, the mid-point, trapezoid and Simpson's have been investigated more recently with the view of obtaining bounds for the quadrature rules in terms of at most second derivative. By using modern theory of inequalities and Peano kernel approach, this thesis is devoted to investigate several refinements inequalities for the Hermite-Hadamard's, Ostrowski's and Simpson's type and deduce explicit bounds for the mid-point, trapezoid and Simpson's quadrature rules in terms of a variety of quasi-convex, s-convex and r-convex mappings, at most second derivative. This approach allows us to investigate several quadrature rules that have restrictions on the behavior of the integrand and thus to deal with larger classes of functions. Several generalizations and improvements for a previous inequalities in the literature for function f where jf0j (or jf0jq; q ¸ 1) is convex (or other type of convexity) hold by applying the H¨older inequality and the power mean inequality. As applications, some error estimates for a proposed quadrature rules and for some special means are derived. A comparison between the presented results with the previous one is considered and discussed. In this way, this thesis provides a study of some of the most famous and fundamental inequalities originated by Hermite-Hadamard, Ostrowski and Simpson and shall gather interesting developments in this research area under a unified framework., Certification of Master's/Doctoral Thesis is not available,Ph.D.
Pages:	154
Call Number:	QA295.A445 2011 tesis
Publisher:	UKM, Bangi
Appears in Collections:	Faculty of Science and Technology / Fakulti Sains dan Teknologi

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.