SavedAdd your journal

Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 50 Issue: 2

The sharper form of a Brunn-Minkowski type inequality for boxes

Gültekin Tınaztepe(AKDENIZ UNIVERSITY)0000-0001-7594-1620
Serap Kemali(AKDENIZ UNIVERSITY)0000-0001-5804-4127
Sevda Sezer(AKDENIZ UNIVERSITY)0000-0001-6448-193X
Zeynep Eken(AKDENİZ ÜNİVERSİTESİ)0000-0002-8939-4653
Pages
—
Publication Date
2021-04-11
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

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

In this study, the Brunn-Minkowski inequality for boxes is studied and a sharper version of this inequality is derived by performing the results based on abstract convexity.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, the Brunn-Minkowski inequality for boxes is studied and a sharper version of this inequality is derived by performing the results based on abstract convexity.
📊
Key Findings & Data:In this study, the Brunn-Minkowski inequality for boxes is studied and a sharper version of this inequality is derived by performing the results based on abstract convexity.
💡
Conclusion & Impact:In this study, the Brunn-Minkowski inequality for boxes is studied and a sharper version of this inequality is derived by performing the results based on abstract convexity.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:abstract concavity · refinement · the Brunn-Minkowski inequality

Abstract

In this study, the Brunn-Minkowski inequality for boxes is studied and a sharper version of this inequality is derived by performing the results based on abstract convexity.

🔖

Cite This Article

Tınaztepe, G., Kemali, S., Sezer, S., Eken, Z. (2021). The sharper form of a Brunn-Minkowski type inequality for boxes. Hacettepe Journal of Mathematics and Statistics, Volume: 50 Issue: 2. https://doi.org/10.15672/hujms.657839

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (22)

  1. G.R. Adilov and S. Kemali, Hermite-Hadamard-Type Inequalities For Increasing Positively Homogeneous Functions, J. Inequal. Appl. 2007, Article ID 21430, 10 pages, 2007.
  2. G.R. Adilov and S. Kemali, Abstract Convexity and Hermite-Hadamard Type Inequalities, J. Inequal. Appl., 2009, Article ID 943534, 13 pages, 2009.
  3. G.R. Adilov and G. Tınaztepe, The Sharpening Some Inequalities via Abstract Convexity, Math. Inequal. Appl. 12, 33–51, 2012.
  4. Y.D. Burago and V.A. Zalgaller, Geometric Inequalities, Springer, 1988.
  5. J.P. Crouzeix, J.E. M. Legaz and M. Volle, Generalized Convexity, Generalized Monotonicity: Recent Results, Kluwer Academic Publishers, 1998.
  6. S.S. Dragomir, J. Dutta and A.M. Rubinov, Hermite-Hadamard Type Inequalities For Increasing Convex Along Rays Functions, Analysis (Munich) 2, 171–181, 2001.
  7. S.S. Dragomir and C.E.M. Pearce, Selected Topics on Hermite–Hadamard Inequalities and Applications, Victoria University, Footscray, Australia, 2000.
  8. S. Jain, K. Mehrez, D. Baleanu and P. Agarwal, Certain Hermite–Hadamard Inequalities for Logarithmically Convex Functions with Applications, Mathematics 7, 163–175, 2019.
  9. S. Jhanthanam, J. Tariboon, S.K. Ntouyas and K. Nonlaopon, On q-Hermite- Hadamard Inequalities for Differentiable Convex Functions, Mathematics 7, 632–641, 2019.
  10. W. Liu, New Integral Inequalities Via $(\alpha,m)$-Convexity and Quasi-Convexity, Hacet. J. Math. Stat. 42, 289–297, 2013.
  11. K. Mehrez and P. Agarwal, New Hermite-Hadamard Type Integral Inequalities for Convex Functions and Their Applications, J. Comput. Appl. Math. 350, 274–285, 2019.
  12. M.E. Özdemir, H. Kavurmacı and E. Set, Ostrowski’s Type Inequalities for $(\alpha,m)$- Convex Functions, Kyungpook Math. J. 50, 371–378, 2010.
  13. Z. Pavic and M.A. Ardıç, The most important inequalities of m-convex functions, Turk. J. Math. 41, 625–635, 2017.
  14. F. Qi and B.Y. Xi, Some Hermite-Hadamard type inequalities for geometrically quasiconvex functions, Proc. Indian Acad. Sci. (Math. Sci.) 124(3), 333–342, 2014.
  15. A.M. Rubinov, Abstract Convexity and Global optimization, Springer US, Kluwer Academic Publishers, 2000.
  16. A.M. Rubinov and Z.Y. Wu, Optimality Conditions in Global Optimization and Their Applications, Math. Program. 120(1), 101–123, 2009.
  17. M.Z. Sarikaya, E. Set, M.E. Özdemir, On new inequalities of Simpson’s Type for s -convex Functions. Comput. Math. Appl. 60, 2191–2199, 2010.
  18. I. Singer, Abstract Convex Analysis, Wiley-Interscience, 1997.
  19. G. Tınaztepe, The sharpening Hölder Inequality via abstract convexity, Turk. J. Math. 40, 438–444, 2016.
  20. I. Yesilce and G.R. Adilov, Hermite-Hadamard Inequalities for $L(j)$-convex Functions and $S(j)$-convex Functions, Malaya J. Mat. 3, 346–359, 2015.
  21. I. Yesilce and G.R. Adilov, Hermite-Hadamard Inequalities for B-convex and $B^{-1}$- convex functions, Int. J. Nonlinear Analysis Appl. 8, 225–233, 2017.
  22. I. Yesilce and G.R. Adilov, Fractional Integral Inequalities for B-convex Functions, Creat. Math. Inform. 26, 345–351, 2017.