TY - JOUR
T1 - On Generalization of Different Integral Inequalities for Harmonically Convex Functions
AU - Reunsumrit, Jiraporn
AU - Vivas-Cortez, Miguel J.
AU - Ali, Muhammad Aamir
AU - Sitthiwirattham, Thanin
N1 - Publisher Copyright:
© 2022 by the authors. Licensee MDPI, Basel, Switzerland.
PY - 2022/2/2
Y1 - 2022/2/2
N2 - In this study, we first prove a parameterized integral identity involving differentiable functions. Then, for differentiable harmonically convex functions, we use this result to establish some new inequalities of a midpoint type, trapezoidal type, and Simpson type. Analytic inequalities of this type, as well as the approaches for solving them, have applications in a variety of domains where symmetry is important. Finally, several particular cases of recently discovered results are discussed, as well as applications to the special means of real numbers.
AB - In this study, we first prove a parameterized integral identity involving differentiable functions. Then, for differentiable harmonically convex functions, we use this result to establish some new inequalities of a midpoint type, trapezoidal type, and Simpson type. Analytic inequalities of this type, as well as the approaches for solving them, have applications in a variety of domains where symmetry is important. Finally, several particular cases of recently discovered results are discussed, as well as applications to the special means of real numbers.
KW - Harmonically convex functions
KW - Midpoint and trapezoidal inequality
KW - Simpson’s inequality
UR - http://www.scopus.com/inward/record.url?scp=85124101556&partnerID=8YFLogxK
U2 - 10.3390/sym14020302
DO - 10.3390/sym14020302
M3 - Article
AN - SCOPUS:85124101556
SN - 2073-8994
VL - 14
JO - Symmetry
JF - Symmetry
IS - 2
M1 - 302
ER -