THE EQUIVALENCE OF THE HERMITE-HADAMARD INEQUALITY TO CHEBYSHEV’S INEQUALITY WITH RESPECT TO THE RIEMANN-STIELTJES INTEGRAL

• المؤلف الرئيسي: IVANAL HAKIM (NIM : 10108035) ; Pembimbing : Prof. Dr. Hendra Gunawan, DENNY
• التنسيق: Final Project
• اللغة: Indonesia
• الوصول للمادة أونلاين: https://digilib.itb.ac.id/gdl/view/15334
• المؤسسة: Institut Teknologi Bandung

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.