Differential q-calculus of Several Variables


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Authors

  • MOHAMMAD W. ALOMARI
  • WASEEM G. ALSHANTI
  • Iqbal Batiha Al Zaytoonah University of Jordan
  • Liliana Guran Department of Hospitality Services, Faculty of Business, Babeș-Bolyai University, Horea street, no. 7, 400174, Cluj- Napoca, Romania.
  • IQBAL H. JEBRIL

Keywords:

q-calculus, q-Gradient, q-Chain Rule, q-Jacobians, q-Hessian, q-Extreme Values

Abstract

This comprehensive investigation explores the application and significance of q-differential calculus in the realm of vector functions of several variables, addressing critical aspects such as q-Rolle’s theorem, the q-Mean-value theorem, and q-chain rule for vector functions. Additionally, we investigate the q-gradient, q-Jacobian, and q-Hessian operators, elucidating their roles in quantifying rates of change, determining directional derivatives, and characterizing critical points of multivariate functions. Furthermore, this research provides a rigorous treatment of Multivariate and Bivariate Taylor theorems in the context of q-differential calculus, presenting analytical expansions of functions around specific points and showcasing their utility in approximating functions in higher dimensions. The q-Maximum and Minimum are demonstrated and discussed as well.

References

Alomari, M.W., Batiha, I.M. & Momani, S. New higher-order implict method for approximating solutions of the initial

value problems. J. Appl. Math. Comput. (2024). https://doi.org/10.1007/s12190-024-02087-3

Haitham Qawaqneh, Mohd Salmi Md Noorani, Hassen Aydi, Amjed Zraiqat, Arslan Hojat Ansari, “On Fixed Point

Results in Partial b-Metric Spaces”, Journal of Function Spaces, vol. 2021, Article ID 8769190, 9 pages, 2021. https://

doi.org/10.1155/2021/8769190

V.G. Kac and P. Cheeung, Quantum calculus, Universitext, Springer-Verlag, New York, (2002).

P.M. Rajković, M.S. Stanković and S.D. Marinković, Mean value theorems in q-calculus, Matematički Vesnik, 54 2002,

–178.

M.W. Alomari, Two-dimensional Pompeiu’s mean value theorems and related results, J. Nonlinear Funct. Anal., 2016

(2016), Article ID 8.

M.W. Alomari, Mean-value theorems in hypercuboid, Commun. Optimization The, Vol 2019 (2019), Article ID 6, pp. 1–11.

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Published

2024-07-25

How to Cite

W. ALOMARI, M., G. ALSHANTI, W., Batiha, I., Liliana Guran, & H. JEBRIL, I. (2024). Differential q-calculus of Several Variables. Results in Nonlinear Analysis, 7(3), 109–129. Retrieved from https://nonlinear-analysis.com/index.php/pub/article/view/431

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