Some New Integral Inequalities Using Quantum Integral Methods

Sahatsathatsana, Chanokgan; Sahatsathatsana, Sattra

doi:10.28924/2291-8639-24-2026-238

Research Article

Some New Integral Inequalities Using Quantum Integral Methods

Chanokgan Sahatsathatsana*
Sattra Sahatsathatsana

* Corresponding author

Abstract

This paper presents new integral inequalities on finite intervals using analytic and elementary quantum integrals. The results extend several well-known classical inequalities as special cases. To support the theoretical findings, numerical examples are included to illustrate their use and provide a clearer understanding.

How to Cite

C. Sahatsathatsana, S. Sahatsathatsana, Some New Integral Inequalities Using Quantum Integral Methods, Int. J. Anal. Appl. 24 (2026), 238. https://doi.org/10.28924/2291-8639-24-2026-238

BibTeX

@article{Sahatsathatsana2026,
  author  = {Sahatsathatsana, Chanokgan and Sahatsathatsana, Sattra},
  title   = {Some New Integral Inequalities Using Quantum Integral Methods},
  journal = {Int. J. Anal. Appl.},
  volume  = {24},
  year    = {2026},
  pages   = {238},
  doi     = {10.28924/2291-8639-24-2026-238}
}

References

[1] F.H. Jackson, On q-Definite Integrals, Q. J. Pure Appl. Math. 4 (1910), 193-203.
[2] F.H. Jackson, q-Difference Equations, Am. J. Math. 32 (1910), 305-314. https://doi.org/10.2307/2370183.
[3] G. Bangerezako, Variational q-Calculus, J. Math. Anal. Appl. 289 (2004), 650-665. https://doi.org/10.1016/j.jmaa.2003.09.004.
[4] H. Gauchman, Integral Inequalities in q-Calculus, Comput. Math. Appl. 47 (2004), 281-300. https://doi.org/10.1016/s0898-1221(04)90025-9.
[5] Y. Miao, F. Qi, Several q-Integral Inequalities, J. Math. Inequal. 1 (2009), 115-121. https://doi.org/10.7153/jmi-03-11.
[6] P. Raychev, R. Roussev, Y. Smirnov, The Quantum Algebra SUq(2) and Rotational Spectra of Deformed Nuclei, J. Phys. G: Nucl. Part. Phys. 16 (1990), L137-L141. https://doi.org/10.1088/0954-3899/16/8/006.
[7] A. Gavrilik, q-Serre Relations in Uq(un) and q-Deformed Meson Mass Sum Rules, J. Phys. A: Math. Gen. 27 (1994), L91-L94. https://doi.org/10.1088/0305-4470/27/3/006.
[8] A. Aral, V. Gupta, R.P. Agarwal, Applications of q-Calculus in Operator Theory, Springer, New York, 2013. https://doi.org/10.1007/978-1-4614-6946-9.
[9] T. Ernst, A Method for q-Calculus, J. Nonlinear Math. Phys. 10 (2003), 487-525. https://doi.org/10.2991/jnmp.2003.10.4.5.
[10] B. Ahmad, S.K. Ntouyas, I.K. Purnaras, Existence Results for Nonlocal Boundary Value Problems of Nonlinear Fractional q-Difference Equations, Adv. Differ. Equ. 2012 (2012), 140. https://doi.org/10.1186/1687-1847-2012-140.
[11] H. Exton, q-Hypergeometric Functions and Applications, Halsted Press, New York, 1983.
[12] D.N. Page, Information in Black Hole Radiation, Phys. Rev. Lett. 71 (1993), 3743-3746. https://doi.org/10.1103/physrevlett.71.3743.
[13] A. Dobrogowska, A. Odzijewicz, Second Order q-Difference Equations Solvable by Factorization Method, J. Comput. Appl. Math. 193 (2006), 319-346. https://doi.org/10.1016/j.cam.2005.06.009.
[14] M. El-Shahed, H. Hassan, Positive Solutions of q-Difference Equation, Proc. Amer. Math. Soc. 138 (2009), 1733-1738. https://doi.org/10.1090/s0002-9939-09-10185-5.
[15] B. Ahmad, Boundary-Value Problems for Nonlinear Third-Order q-Difference Equations, Electron. J. Differ. Equ. 2011 (2011), 94.
[16] T. Ernst, A Comprehensive Treatment of q-Calculus, Springer, Basel, 2012. https://doi.org/10.1007/978-3-0348-0431-8.
[17] U. Ji, Quantum Extensions of Fourier-Gauss and Fourier-Mehler Transforms, J. Korean Math. Soc. 45 (2008), 1785-1801. https://doi.org/10.4134/jkms.2008.45.6.1785.
[18] C. Sahatsathatsana, S. Sahatsathatsana, On Quantum Montgomery and Ostrowski-Type Inequalities for Uniformly Convex Functions, Int. J. Anal. Appl. 24 (2026), 188. https://doi.org/10.28924/2291-8639-24-2026-188.
[19] C. Sahatsathatsana, P. Yotkaew, New Estimates of the q-Hermite–Hadamard Inequalities via Strong Convexity, Axioms 14 (2025), 576. https://doi.org/10.3390/axioms14080576.
[20] V.G. Kac, P. Cheung, Quantum Calculus, Springer, New York, 2000. https://doi.org/10.1007/978-1-4613-0071-7.
[21] J. Tariboon, S.K. Ntouyas, Quantum Calculus on Finite Intervals and Applications to Impulsive Difference Equations, Adv. Differ. Equ. 2013 (2013), 282. https://doi.org/10.1186/1687-1847-2013-282.
[22] J. Tariboon, S.K. Ntouyas, Quantum Integral Inequalities on Finite Intervals, J. Inequal. Appl. 2014 (2014), 121. https://doi.org/10.1186/1029-242x-2014-121.
[23] Q.A. Ngô, D.D. Thang, T.T. Dat, D.A. Tuan, Note on an Integral Inequality, J. Inequal. Pure Appl. Math. 7 (2006), 120.
[24] W.J. Liu, G.S. Cheng, C.C. Li, Further Development of an Open Problem Concerning an Integral Inequality, J. Inequal. Pure Appl. Math. 9 (2008), 14.
[25] L. Bougoffa, Note on an Open Problem, J. Inequal. Pure Appl. Math. 8 (2007), 58.
[26] K. Boukerrioua, A. Guezane-Lakoud, On an Open Question Regarding an Integral Inequality, J. Inequal. Pure Appl. Math. 8 (2007), 77.
[27] W.J. Liu, C.C. Li, J.W. Dong, On an Open Problem Concerning an Integral Inequality, J. Inequal. Pure Appl. Math. 8 (2007), 74.
[28] W.J. Liu, G.S. Cheng, C.C. Li, Further Development of an Open Problem, J. Inequal. Pure Appl. Math. 9 (2008), 108.
[29] K. Brahim, On Some q-Integral Inequalities, J. Inequal. Pure Appl. Math. 9 (2008), 106.