Analysis of Quantum Multiplicative Calculus and Related Inequalities

Muhammad Nasim Aftab, Saad Ihsan Butt, Mohammed Alammar and Youngsoo Seol ()
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Muhammad Nasim Aftab: Department of Mathematics, University of Engineering and Technology, Lahore 54000, Pakistan
Saad Ihsan Butt: Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore 54000, Pakistan
Mohammed Alammar: Applied College, Shaqra University, Shaqra 11961, Saudi Arabia
Youngsoo Seol: Department of Mathematics, Dong-A University, Busan 49315, Republic of Korea

Mathematics, 2025, vol. 13, issue 21, 1-20

Abstract: This article investigates the exact meaning of a quantum derivative result and the corresponding definition of a quantum definite integral in multiplicative calculus from a geometrical viewpoint. After this critical analysis, we give an accurate definition of the q -multiplicative definite integral and the corresponding derivative result. Additionally, an example pertaining to q -multiplicative definite integrals is presented, and rigorous analysis to prove several fundamental results is provided. In addition, two other concepts are defined: the left q -multiplicative derivative and definite integral and the right q -multiplicative derivative and definite integral. Finally, several q -multiplicative Hermite–Hadamard-type inequalities are constructed, and related examples are shown to support our recent findings.

Keywords: q-multiplicative calculus; multiplicative calculus; geometric calculus; Hermite–Hadamard inequality (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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