engleski

Hermite-Hadamard -Fejér type inequalities for higher order convex functions and quadrature formulae

Over the last decades, Hermite-Hadamard type inequalities and Hermite-Hadamard-Fejér type inequalities have been extensively investigated and applied in approximation theory, special means theory, optimization theory, information theory, and numerical analysis. The main purpose of this talk is to present some new Hermite-Hadamard-Fejér type inequalities for higher-order convex functions and the general weighted integral formula involving w-harmonic sequences of functions. Since a special case of the obtained integral formula is the general weighted Euler integral identity, we also derive Hermite- Hadamard-Fejér type inequalities for the general three, four, and five-point quadrature formulae of Euler type. Further, we establish Hermite- Hadamard-Fejér type inequalities for the corrected three-point formula, the corrected four- point formula, and the corrected five-point quadrature formula of the Euler type. These formulae include not only the values of the function in the chosen points but also the values of the first derivative at the endpoints of the interval, so have a degree of exactness higher than the adjoint original formulae. Finally, certain special cases will be presented such as Hermite-Hadamard-Fejér type estimates for Simpson, Maclaurin, corrected Simpson, and corrected Maclaurin quadrature rules.

Hermite-Hadamard-Fejér inequalities, higher order convex functions, quadrature formulae.

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