Naslov
Applications of the weighted Hermite-Hadamard inequality for higher order convex functions in deriving new estimates for various quadrature formulas

Autori
Barić, Josipa

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

Izvornik
Proceedings of TheIIER International Conference, Lisbon, Portugal / Prusty, Manas Ranjan - Bhubaneswar, India : Institute for Technology and Research (ITRESEARCH) / - , 2022, 1-1

Skup
1407 IIER International Conference on Applied Physics and Mathematics

Mjesto i datum
Lisabon, Portugal, 29.09.2022. - 30.09.2022

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
Hermite-Hadamard’s inequality, Higher Order Convex Function, Harmonic Sequence, Quadrature Formula, Weighted Function

Sažetak
The theory of convex function is at its core a theory about comparing arithmetic means (of certain random variables with their composition by a given function). The well known Hermite-Hadamard inequality gives us an estimate of the (integral) mean value of a continuous convex function. Hermite-Hadamard’s inequality was first noticed by Ch. Hermite in 1883 and rediscovered ten years later by J. Hadamard. It is interesting that each of the two sides of Hermite-Hadamard’s inequality characterizes convex functions. In this talk, new estimates for some quadrature rules (integral identities for numerical calculation of the definite integral) are presented using the weighted Hermite-Hadamard inequality for higher order convex functions and weighted version of the integral identity expressed by w-harmonic sequences of functions. Applying obtained results on some special cases of the weight functions new estimates of various classical quadrature formulas are given in several examples.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA