TY - JOUR
T1 - On some new simpson’s formula type inequalities for convex functions in post-quantum calculus
AU - Vivas-Cortez, Miguel J.
AU - Ali, Muhammad Aamir
AU - Qaisar, Shahid
AU - Sial, Ifra Bashir
AU - Jansem, Sinchai
AU - Mateen, Abdul
N1 - Publisher Copyright:
© 2021 by the authors. Licensee MDPI, Basel, Switzerland.
PY - 2021/12/14
Y1 - 2021/12/14
N2 - In this work, we prove a new (p, q)-integral identity involving a (p, q)-derivative and (p, q)-integral. The newly established identity is then used to show some new Simpson’s formula type inequalities for (p, q)-differentiable convex functions. Finally, the newly discovered results are shown to be refinements of comparable results in the literature. Analytic inequalities of this type, as well as the techniques used to solve them, have applications in a variety of fields where symmetry is important.
AB - In this work, we prove a new (p, q)-integral identity involving a (p, q)-derivative and (p, q)-integral. The newly established identity is then used to show some new Simpson’s formula type inequalities for (p, q)-differentiable convex functions. Finally, the newly discovered results are shown to be refinements of comparable results in the literature. Analytic inequalities of this type, as well as the techniques used to solve them, have applications in a variety of fields where symmetry is important.
KW - Convex functions
KW - Post-quantum calculus
KW - Simpson’s inequalities
UR - http://www.scopus.com/inward/record.url?scp=85121500088&partnerID=8YFLogxK
U2 - 10.3390/sym13122419
DO - 10.3390/sym13122419
M3 - Article
AN - SCOPUS:85121500088
SN - 2073-8994
VL - 13
JO - Symmetry
JF - Symmetry
IS - 12
M1 - 2419
ER -