TY - JOUR
T1 - Some new hermite–hadamard and related inequalities for convex functions via (P, q)-integral
AU - Vivas-Cortez, Miguel
AU - Ali, Muhammad Aamir
AU - Budak, Hüseyin
AU - Kalsoom, Humaira
AU - Agarwal, Praveen
N1 - Publisher Copyright:
© 2021 by the authors. Licensee MDPI, Basel, Switzerland.
PY - 2021/7
Y1 - 2021/7
N2 - In this investigation, for convex functions, some new (p, q)–Hermite–Hadamard-type inequalities using the notions of (p, q)π2 derivative and (p, q)π2 integral are obtained. Furthermore, for (p, q)π2-differentiable convex functions, some new (p, q) estimates for midpoint and trapezoidal-type inequalities using the notions of (p, q)π2 integral are offered. It is also shown that the newly proved results for p = 1 and q → 1− can be converted into some existing results. Finally, we discuss how the special means can be used to address newly discovered inequalities.
AB - In this investigation, for convex functions, some new (p, q)–Hermite–Hadamard-type inequalities using the notions of (p, q)π2 derivative and (p, q)π2 integral are obtained. Furthermore, for (p, q)π2-differentiable convex functions, some new (p, q) estimates for midpoint and trapezoidal-type inequalities using the notions of (p, q)π2 integral are offered. It is also shown that the newly proved results for p = 1 and q → 1− can be converted into some existing results. Finally, we discuss how the special means can be used to address newly discovered inequalities.
KW - (p, q) estimates for midpoint and trapezoidal type inequalities
KW - Post-quantum calculus
KW - Quantum calculus
UR - http://www.scopus.com/inward/record.url?scp=85109392528&partnerID=8YFLogxK
U2 - 10.3390/e23070828
DO - 10.3390/e23070828
M3 - Article
AN - SCOPUS:85109392528
SN - 1099-4300
VL - 23
JO - Entropy
JF - Entropy
IS - 7
M1 - 828
ER -