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Some new error bounds for Hermite-Hadamard inequality and numerical integration formulas in quantum multiplicative calculus with computational analysis.

  • Published In: Mathematics in Engineering, Science & Aerospace (MESA), 2025, v. 16, n. 3. P. 913 1 of 3

  • Database: Academic Search Ultimate 2 of 3

  • Authored By: Hussain, Mubashir; Agarwal, Praveen; Aslam, Asna; Haibo Chen 3 of 3

Abstract

This study presents a novel q-multiplicative calculus by merging the concepts of quantum and multiplicative calculus. This framework is crucial for phenomena that require discrete scaling and multiplicative differentiation, such as in biology, fractals, quantum mechanics, and finance. We present the q-multiplicative derivative, q-multiplicative integral, and their fundamental properties with their proofs. These definitions aid in the presentation of new versions of Hermite Hadamard and midpoint inequalities. The generalized version of the Hermite-Hadamard inequality forg-multiplicative calculus has been established. In addition, a graphical and numerical analysis verifies the validity and effectiveness of the newly defined inequalities. We provide a detailed overview of the newly formed results and discussed the behavior of these inequalities based on various set parameters, numerically and graphically. Based on its applicability and effectiveness to complex systems, this work will greatly attract future research and exploration in this field. [ABSTRACT FROM AUTHOR]

Additional Information

  • Source:Mathematics in Engineering, Science & Aerospace (MESA). 2025/09, Vol. 16, Issue 3, p913
  • Document Type:Article
  • Subject Area:History
  • Publication Date:2025
  • ISSN:2041-3165
  • Accession Number:188142407
  • Copyright Statement:Copyright of Mathematics in Engineering, Science & Aerospace (MESA) is the property of Nonlinear Studies and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

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