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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| Format: | Final Project |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/15334 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | 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. |
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