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https://ptsldigital.ukm.my/jspui/handle/123456789/499574| Title: | On approximating of the Riemann-Stieltjes double integral |
| Authors: | Yousef Mohammad Hammad Jawarneh (P42292) |
| Supervisor: | Mohd Salmi Noorani, Prof. Dr. |
| Keywords: | Integrals Riemann-Stieltjes Mappings Cubature rules Riemann integrals |
| Issue Date: | 1-Dec-2015 |
| Description: | The concept of Riemann-Stieltjes integrals is a very important problem that arises in many scientific, financial and engineering applications. The research conducted in this thesis is designed to study the approximation problem of the Riemann-Stieltjes double integrals in terms of Riemann-Stieltjes double sums. The fundamental aim is to establish several cubature rules for various mappings of two variables. The approximation problem of Riemann-Stieltjes integral R b a f (t) du (t); where f is called the integrand, u is called the integrator, plays an important role in mathematics. The approximation problem of the Riemann-Stieltjes integral in terms of the Riemann-Stieltjes sums have been considered recently by many authors. However, a small attention and a few works have been considered for mappings of two variables; i.e., the approximation problem of the Riemann-Stieltjes double integral R b a R d c f (t; s) dsdtu (t; s) in terms of the Riemann-Stieltjes double sums. This study is devoted to obtain several bounds for R b a R d c f (t; s) dsdtu (t; s) under various assumptions on the integrand f and the integrator u. Mainly, the concepts of bounded variation and bi-variation are used at large in the thesis. Several proposed cubature formula are introduced to approximate such double integrals. For mappings of two variables several inequalities of Trapezoid, Gruss and Ostrowski type for mappings of bounded variation, bounded bi-variation, Lipschitzian and monotonic are introduced and discussed. Namely, Trapezoid-type rules for RS-Double integrals are proved, and therefore the classical Hermite-Hadamard inequality for mappings of two variables is established. A Korkine type identity is used to obtain several Gruss type inequalities for integrable functions. Finally, approximating real functions of two variables which possess n-th partial derivatives of bounded bi-variation, Lipschitzian and absolutely continuous are established and investigated.,Ph.D. |
| Pages: | 146 |
| Call Number: | QA311.J348 2015 tesis |
| Publisher: | UKM, Bangi |
| Appears in Collections: | Faculty of Science and Technology / Fakulti Sains dan Teknologi |
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