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

Autori
Barić, Josipa ; Kvesić, Ljiljanka ; Pečarić, Josip ; Ribičić Penava, Mihaela

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni

Izvornik
Book of abstracts of International Conference on Mathematics and Mathematics Education / DOĞAN, Nurettin ; ÖZKAN, Mustafa - Ankara : Gazi University, 2021, 89-90

Skup
1st International Conference of Mathematics and Mathematics Education

Mjesto i datum
Ankara, Turska, 16.09.2021. - 18.09.2021

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

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

Sažetak
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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA