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Journals / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2026 / Volume: 68 Issue: 1

The Minkowski's inequalities utilizing newly defined generalized fractional integral operators

Fuat Usta0000-0002-7750-6910
Hüseyin Budak0000-0002-7750-6910
Fatma Ertugral0000-0002-7561-8388
Mehmet Zeki Sarıkaya0000-0002-6165-9242
Pages
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Publication Date
2019-02-01
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Within this context, we provide new upper bounds of inequalities utilizing generalized fractional integral operators and show and state other inequalities related to this fractional integral operator.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Motivated by the recent generalized fractional integral operators proposed by Tunc et. al. <cite>tunc</cite>, we establish a generalization of the reverse Minkowski's inequalities.
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Key Findings & Data:Motivated by the recent generalized fractional integral operators proposed by Tunc et. al. <cite>tunc</cite>, we establish a generalization of the reverse Minkowski's inequalities.
💡
Conclusion & Impact:Within this context, we provide new upper bounds of inequalities utilizing generalized fractional integral operators and show and state other inequalities related to this fractional integral operator.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Fractional integral operators · Hermite-Hadamard inequality · midpoint inequality

Abstract

Motivated by the recent generalized fractional integral operators proposed by Tunc et. al. <cite>tunc</cite>, we establish a generalization of the reverse Minkowski's inequalities. Within this context, we provide new upper bounds of inequalities utilizing generalized fractional integral operators and show and state other inequalities related to this fractional integral operator.

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Cite This Article

Usta, F., Budak, H., Ertugral, F., Sarıkaya, M. Z. (2019). The Minkowski's inequalities utilizing newly defined generalized fractional integral operators. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 68 Issue: 1. https://doi.org/10.31801/cfsuasmas.463983

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References (22)

  1. R. P. Agarwal, M.-J. Luo and R. K. Raina, On Ostrowski type inequalities, Fasciculi Mathematici, 24, De Gruyter, (2016) doi:10.1515/fascmath-2016-0001.
  2. P. Agarwal and J. E. Restrepo, An extension by means of ω-weighted classes of the generalized Riemann-Liouville k-fractional integral inequalities, (pending).
  3. A. Akkurt, M. E. Yıldırım, and H. Yıldırım, On some integral inequalities for (k,h)-Riemann-Liouville fractional integral, New Trends in Mathematical Science, 4 (2016), no. 2, 138--138.
  4. L. Bougoffa, On Minkowski and Hardy integral inequality, J. Inequal. Pure and Appl. Math. 7 (2006).
  5. V.L. Chinchane, New approach to Minkowski fractional inequalities using generalized kfractional integral operator, arXiv:1702.05234v1 [math.CA].
  6. V.L. Chinchane and D. B. Pachpatte, New fractional inequalities via Hadamard fractional integral, Internat. J. Functional Analyisis, Operator Theory and Application, 5(3)(2013), 165-176.
  7. Z. Dahmani, On Minkowski and Hermite-Hadamard integral inequalities via fractional integration, Ann. Funct. Anal., 1(1)(2010), 51-58.
  8. R. Diaz and E. Pariguan, On hypergeometric functions and Pochhammer k symbol, Divulg.Math, 15, (2007), 179- 192.
  9. U. Katugampola, New approach to a generalized fractional integral, Applied Mathematics and Computation (2011).xxxxxxxxxxx
  10. U. Katugampola, On Generalized Fractional Integrals and Derivatives, Ph.D. Dissertation, Southern Illinois University, Carbondale, August, 2011.
  11. R. Khalil, M. Al horani, A. Yousef, M. Sababheh, A new definition of fractional derivative, Journal of Computational Apllied Mathematics, 264 (2014), 65-70.
  12. A. A. Kilbas, H.M. Srivastava and J.J. Trujillo, Theory and Applications of Fractional Diferential Equations, Elsevier B.V., Amsterdam, Netherlands, 2006.
  13. V. Kiryakova, On two Saigos fractional integral operator in the class of univalent functions, Fract. Calc. Appl. Anal., 9(2)(2006), 159-176.
  14. H. Kober, On fractional integrals and derivatives, The Quarterly Journal of Mathematics (Oxford Series), (1940). xxxxxxxxxxxxxxx
  15. S. Mubeen and G. M. Habibullah, k-Fractional integrals and applications, International Journal of Contemporary Mathematical Sciences, 7(2012), 89--94.
  16. E. Set, M. Tomar, M. Sarikaya, On generalized Gruss type inequalities for k-fractional integrals, Appl. Math. Comput. (2015) xxxxxxxxxxxxxxx
  17. M. Saigo, A remark on integral operators involving the Gauss hypergeometric function, Rep. College General Ed., Kyushu Univ., 11 (1978), 135-143.
  18. M. Sarikaya, Z. Dahmani, M. Kiris, F. Ahmad, (k; s)-Riemann-Liouville fractional integral and applications, Hacet. J. Math. Stat., (2016) xxxxxxxxxxxxxxxxx
  19. B. Sroysang, More on Reverses of Minkowskis Integral Inequality, Mathematica Aeterna, Vol. 3, (2013), no. 7, 597-600.
  20. W. T. Sulaiman, Reverses of Minkowski's, Hölder's, and Hardy's integral inequalities, Int. J. Mod. Math. Sci., (2012), 1(1), 1424.
  21. R.K. Raina, On generalized Wright's hypergeometric functions and fractional calculus operators, East Asian Math. J., 21(2) (2005), 191-203.
  22. T. Tunç, H. Budak, F. Usta, M. Z. Sarikaya, On new generalized fractional integral operators and related fractional inequalities, ResearchGate Article, Available online at: https://www.researchgate.net/publication/313650587.