KaydedilenlerDerginizi ekleyin

Dergiler / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 50 Issue: 5

The Hermite-Hadamard inequalities for $p$-convex functions

Zeynep Eken(AKDENIZ UNIVERSITY)0000-0002-8939-4653
Serap Kemali(AKDENIZ UNIVERSITY)0000-0001-5804-4127
Gültekin Tınaztepe(AKDENIZ UNIVERSITY)0000-0001-7594-1620
Gabil Adilov(AKDENIZ UNIVERSITY)0000-0003-3012-6176
Sayfa
—
Yayın Tarihi
2021-10-15
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Some inequalities for these functions are expressed.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In this paper, the Hermite-Hadamard inequality for $p-$convex function is provided.
📊
Temel Bulgular & Veri:Some integral inequalities for them are also presented.
💡
Sonuç & Katkı:Some inequalities for these functions are expressed.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Hermite-Hadamard Inequality · Convex set · Convex functions

Abstract

In this paper, the Hermite-Hadamard inequality for $p-$convex function is provided. Some integral inequalities for them are also presented. Also, based on the integral and double integral of $p-$convex sets, the new functions are defined and under certain conditions, $p-$convexity of these functions are shown. Some inequalities for these functions are expressed.

🔖

Bu Makaleye Atıf Yap

Eken, Z., Kemali, S., Tınaztepe, G., Adilov, G. (2021). The Hermite-Hadamard inequalities for $p$-convex functions. Hacettepe Journal of Mathematics and Statistics, Volume: 50 Issue: 5. https://doi.org/10.15672/hujms.775508

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (26)

  1. G. Adilov and S. Kemali, Abstract convexity and Hermite-Hadamard type inequalities, J. Inequal.Appl. 2009, Article ID 943534, 13 pages, 2009.
  2. G. Adilov and I. Yesilce, $B^{-1}$-convex Sets and $B^{-1}$-measurable Maps., Numer. Func. Anal. Opt. 33 (2), 131–141, 2012.
  3. J.B. Jesús Bastero and A. Peña, The Theorems of Caratheodory and Gluskin for $0<p<1$, Proc. Amer. Math. Soc. 123 (1), 141–144, 1995.
  4. G. Birkhoff and M.K. Bennett, The convexity lattice of a poset, Order 2 (3), 223–242, 1985.
  5. W. Briec and C. Horvath, Nash points, Ky Fan inequality and equilibria of abstract economies in Max-Plus and B-convexity, J. Math. Anal. App. 341 (1), 188–199, 2008.
  6. S.S. Dragomir, Inequalities of Hermite-Hadamard type for GG-convex functions, Indian J. Math. 60 (1), 1–21, 2018.
  7. S.S. Dragomir, Inequalities of Hermite-Hadamard type for GH-convex functions, Electron. J. Math. Anal. Appl. 7 (2), 244–255, 2019.
  8. S.S. Dragomir and B.T. Torebek, Some Hermite-Hadamard type inequalities in the class of hyperbolic p-convex functions, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 1130 (4), 3413–3423, 2019.
  9. S.S. Dragomir and C. Pearce, Selected topics on Hermite-Hadamard inequalities and applications, RGMIA Monographs, Victoria University, 2000.
  10. S.S. Dragomir and S. Fitzpatrick, Hadamard’s inequality for s-convex functions in the first sense and applications, Demonstr. Math. 31 (3), 633–642, 1998.
  11. S.S. Dragomir and S. Fitzpatrick, The Hadamard inequalities for s-convex functions in the second sense. Demonstr. Math. 32 (4), 687–696, 1999.
  12. X.C. Huang and X.P. Zhou, Probabilistic assessment for slope using the generalized Chebyshev inequalities, Int. J. Geomec. 20 (4), 06020003, 2020.
  13. I. Kawai, Locally convex lattices, J. Math. Soc. Jpn. 9 (3), 281–314, 1957.
  14. S. Kemali, G. Tinaztepe and G. Adilov, New Type Inequalities for $B^{-1}$-convex Functions involving Hadamard Fractional Integral, Facta Univ-Ser. Math. Informat. 33 (5), 697–704, 2019.
  15. S. Kemali, I. Yesilce and G. Adilov, $B$-Convexity, $B^{-1}$-Convexity, and Their Comparison, Numer. Func. Anal. Opt. 36 (2), 133–146, 2015.
  16. T. Migot and M. G. Cojocaru, A parametrized variational inequality approach to track the solution set of a generalized nash equilibrium problem, Eur. J. Oper. Res. 283 (3), 1136–1147, 2020.
  17. S. Nayak, The Hadamard determinant inequality-Extensions to operators on a Hilbert space, J. Func. Analysis 274 (10), 2978–3002, 2018.
  18. H. Ogasawara, The multivariate Markov and multiple Chebyshev inequalities, Commu. Stat. Theory 49 2, 441–453, 2020.
  19. S. Sezer, Z. Eken, G. Tnaztepe and G. Adilov, $p$-convex functions and their some properties, Numer. Func. Anal. Opt. 42 (4), 443–459, 2021. DOI: 10.1080/01630563.2021.1884876.
  20. W. Takahashi, A convexity in metric space and nonexpansive mappings. I., Kodai Math. Sem. Rep. 22 (2), 142–149, 1970. DOI: 10.2996/kmj/1138846111
  21. Y. User and K. Gulez, A new direct torque control algorithm for torque and flux ripple reduction, Int. Rev. Elect. Eng. 8 (4), 644–653, 2013.
  22. J. G. Wendel, Note on the gamma function, Amer. Math. Monthly 55 (9), 563–564, 1948.
  23. I. Yesilce and G. Adilov, Hermite-Hadamard inequalities for $B$-convex and $B^{-1}$- convex functions, Int. J. Nonlinear Anal. Appl. 8, 225–233, 2017.
  24. I. Yesilce and G. Adilov, Hermite-Hadamard type inequalities for $B^{-1}$-convex functions involving generalized fractional integral operators, Filomat 32 (18), 6457–6464, 2018.
  25. I. Yesilce and G. Adilov, Hermite-Hadamard Inequalities for L (j)-convex Functions and S (j)-convex Functions, Malaya J. Mat. 3 (3), 346–359, 2015.
  26. A.M. Zaki, A.M. El-Nagar, M. El-Bardini and F.A.S. Soliman, Deep learning controller for nonlinear system based on Lyapunov stability criterion, Neural Comput. Appl. 33, 1515–1531, 2021.