Simpson- and Newton-Type Inequalities for Convex Functions via (p,q)-Calculus
Open Access
- 9 June 2021
- journal article
- research article
- Published by MDPI AG in Mathematics
- Vol. 9 (12) , 1338
Abstract
In this paper, we establish several new -integral identities involving -integrals by using the definition of a -derivative. These results are then used to derive -integral Simpson- and Newton-type inequalities involving convex functions. Moreover, some examples are given to illustrate the investigated results.
Keywords
This publication has 52 references indexed in Scilit:
- Some quantum estimates for Hermite–Hadamard inequalitiesApplied Mathematics and Computation, 2015
- Quantum integral inequalities on finite intervalsJournal of Inequalities and Applications, 2014
- Quantum calculus on finite intervals and applications to impulsive difference equationsAdvances in Difference Equations, 2013
- Several q-integral inequalitiesJournal of Mathematical Inequalities, 2007
- Integral inequalities in q-calculusComputers & Mathematics with Applications, 2004
- Variational q-calculusJournal of Mathematical Analysis and Applications, 2004
- On Simpson's inequality and applicationsJournal of Inequalities and Applications, 2000
- q-Serre relations in Uq(un) and q-deformed meson mass sum rulesJournal of Physics A: General Physics, 1994
- A (p, q)-oscillator realization of two-parameter quantum algebrasJournal of Physics A: General Physics, 1991
- The quantum algebra SUq(2) and rotational spectra of deformed nucleiJournal of Physics G: Nuclear and Particle Physics, 1990