TY - JOUR
T1 - Some Hermite-Hadamard and midpoint type inequalities in symmetric quantum calculus
AU - Butt, Saad Ihsan
AU - Aftab, Muhammad Nasim
AU - Nabwey, Hossam A.
AU - Etemad, Sina
N1 - Publisher Copyright:
© 2024 the Author(s), licensee AIMS Press.
PY - 2024
Y1 - 2024
N2 - The Hermite-Hadamard inequalities are common research topics explored in different dimensions. For any interval [b0, b1 ] ⊂ ℜ, we construct the idea of the Hermite-Hadamard inequality, its different kinds, and its generalization in symmetric quantum calculus at b0 ∈ [b0, b1 ] ⊂ℜ. We also construct parallel results for the Hermite-Hadamard inequality, its different types, and its generalization on other end point b1, and provide some examples as well. Some justification with graphical analysis is provided as well. Finally, with the assistance of these outcomes, we give a midpoint type inequality and some of its approximations for convex functions in symmetric quantum calculus.
AB - The Hermite-Hadamard inequalities are common research topics explored in different dimensions. For any interval [b0, b1 ] ⊂ ℜ, we construct the idea of the Hermite-Hadamard inequality, its different kinds, and its generalization in symmetric quantum calculus at b0 ∈ [b0, b1 ] ⊂ℜ. We also construct parallel results for the Hermite-Hadamard inequality, its different types, and its generalization on other end point b1, and provide some examples as well. Some justification with graphical analysis is provided as well. Finally, with the assistance of these outcomes, we give a midpoint type inequality and some of its approximations for convex functions in symmetric quantum calculus.
KW - convex functions
KW - Hermite-Hadamard inequality
KW - symmetric quantum calculus
UR - https://www.scopus.com/pages/publications/85183922162
U2 - 10.3934/math.2024268
DO - 10.3934/math.2024268
M3 - Article
AN - SCOPUS:85183922162
SN - 2473-6988
VL - 9
SP - 5523
EP - 5549
JO - AIMS Mathematics
JF - AIMS Mathematics
IS - 3
ER -