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• W2522396661 abstract "The concept of Riemann-Stieltjes integral $int_a^b {fleft( t right)duleft( t right)}$; 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 $int_a^b {fleft( t right)duleft( t right)}$ 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 $int_a^b {int_c^d {fleft( {t,s} right)d_s d_t uleft( {t,s} right)} }$ in terms of the Riemann-Stieltjes double sums. This study is devoted to obtain several bounds for $int_a^b {int_c^d {fleft( {t,s} right)d_s d_t uleft( {t,s} right)} }$ 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 $mathcal{RS}$-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." @default.
• W2522396661 created "2016-09-30" @default.
• W2522396661 creator A5073339965 @default.
• W2522396661 date "2016-09-16" @default.
• W2522396661 modified "2023-09-27" @default.
• W2522396661 title "Numerous approximations of Riemann-Stieltjes double integrals" @default.
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