A Symmetric Quantum Perspective of Analytical Inequalities and Their Applications

Muhammad Zakria Javed, Nimra Naeem, Muhammad Uzair Awan, Yuanheng Wang () and Omar Mutab Alsalami
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Muhammad Zakria Javed: Department of Mathematics, Government College University Faisalabad, Faisalabad 38000, Pakistan
Nimra Naeem: Department of Mathematics, Government College University Faisalabad, Faisalabad 38000, Pakistan
Muhammad Uzair Awan: Department of Mathematics, Government College University Faisalabad, Faisalabad 38000, Pakistan
Yuanheng Wang: School of Mathematical Sciences, Zhejiang Normal University, Jinhua 321004, China
Omar Mutab Alsalami: Department of Electrical Engineering, College of Engineering, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia

Mathematics, 2025, vol. 13, issue 18, 1-22

Abstract: This study explores some new symmetric quantum inequalities that are based on Breckner’s convexity. By using these concepts, we propose new versions of Hermite–Hadamard (H-H) and Fejer-type inequalities. Additionally, we establish a new integral identity which helped us to derive a set of new quantum inequalities. Using the symmetric quantum identity, Breckner’s convexity, and several other classical inequalities, we develop blended bounds for a general quadrature scheme. To ensure the significance of this study, a few captivating applications are discussed.

Keywords: Symmetric quantum calculus; Hermite–Hadamard inequality; Fejér inequality; Error bounds; Breckner’s convexity (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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