THE EQUIVALENCE OF THE HERMITE-HADAMARD INEQUALITY TO CHEBYSHEV̉̉S INEQUALITY WITH RESPECT TO THE RIEMANN-STIELTJES INTEGRAL
The Hermite-Hadamard inequality is an inequality for convex functions that gives an estimate for the integral mean value of a convex function on a closed interval by its value at the middle of interval and the average of its values at the endpoints. In this final project, we present a generalization...
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id-itb.:153342017-09-27T11:42:59ZTHE EQUIVALENCE OF THE HERMITE-HADAMARD INEQUALITY TO CHEBYSHEVÃâÃâS INEQUALITY WITH RESPECT TO THE RIEMANN-STIELTJES INTEGRAL IVANAL HAKIM (NIM : 10108035) ; Pembimbing : Prof. Dr. Hendra Gunawan, DENNY Indonesia Final Project INSTITUT TEKNOLOGI BANDUNG https://digilib.itb.ac.id/gdl/view/15334 The Hermite-Hadamard inequality is an inequality for convex functions that gives an estimate for the integral mean value of a convex function on a closed interval by its value at the middle of interval and the average of its values at the endpoints. In this final project, we present a generalization of the Hermite-Hadamard inequality and Chebyshev’s inequality with respect to the Riemann-Stieltjes integral. We also prove that the Hermite-Hadamard inequality and Chebyshev’s inequality imply each other. In addition, we also present an application of the Hermite-Hadamard inequality with respect to the Riemann-Stieltjes integral for estimating the power mean of n positive real numbers by the aritmethic mean. text |
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The Hermite-Hadamard inequality is an inequality for convex functions that gives an estimate for the integral mean value of a convex function on a closed interval by its value at the middle of interval and the average of its values at the endpoints. In this final project, we present a generalization of the Hermite-Hadamard inequality and Chebyshev’s inequality with respect to the Riemann-Stieltjes integral. We also prove that the Hermite-Hadamard inequality and Chebyshev’s inequality imply each other. In addition, we also present an application of the Hermite-Hadamard inequality with respect to the Riemann-Stieltjes integral for estimating the power mean of n positive real numbers by the aritmethic mean. |
| format |
Final Project |
| author |
IVANAL HAKIM (NIM : 10108035) ; Pembimbing : Prof. Dr. Hendra Gunawan, DENNY |
| spellingShingle |
IVANAL HAKIM (NIM : 10108035) ; Pembimbing : Prof. Dr. Hendra Gunawan, DENNY THE EQUIVALENCE OF THE HERMITE-HADAMARD INEQUALITY TO CHEBYSHEV̉̉S INEQUALITY WITH RESPECT TO THE RIEMANN-STIELTJES INTEGRAL |
| author_facet |
IVANAL HAKIM (NIM : 10108035) ; Pembimbing : Prof. Dr. Hendra Gunawan, DENNY |
| author_sort |
IVANAL HAKIM (NIM : 10108035) ; Pembimbing : Prof. Dr. Hendra Gunawan, DENNY |
| title |
THE EQUIVALENCE OF THE HERMITE-HADAMARD INEQUALITY TO CHEBYSHEV̉̉S INEQUALITY WITH RESPECT TO THE RIEMANN-STIELTJES INTEGRAL |
| title_short |
THE EQUIVALENCE OF THE HERMITE-HADAMARD INEQUALITY TO CHEBYSHEV̉̉S INEQUALITY WITH RESPECT TO THE RIEMANN-STIELTJES INTEGRAL |
| title_full |
THE EQUIVALENCE OF THE HERMITE-HADAMARD INEQUALITY TO CHEBYSHEV̉̉S INEQUALITY WITH RESPECT TO THE RIEMANN-STIELTJES INTEGRAL |
| title_fullStr |
THE EQUIVALENCE OF THE HERMITE-HADAMARD INEQUALITY TO CHEBYSHEV̉̉S INEQUALITY WITH RESPECT TO THE RIEMANN-STIELTJES INTEGRAL |
| title_full_unstemmed |
THE EQUIVALENCE OF THE HERMITE-HADAMARD INEQUALITY TO CHEBYSHEV̉̉S INEQUALITY WITH RESPECT TO THE RIEMANN-STIELTJES INTEGRAL |
| title_sort |
equivalence of the hermite-hadamard inequality to chebyshevãâãâs inequality with respect to the riemann-stieltjes integral |
| url |
https://digilib.itb.ac.id/gdl/view/15334 |
| _version_ |
1822017822780293120 |