SavedAdd your journal

Journals / Hacettepe Journal of Mathematics and Statistics / 2021 / Cilt: 50 - Sayı: 5

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

Zeynep Eken
Gabil Adilov
Serap Kemali
Gültekin Tınaztepe
Pages
1268–1279
Publication Date
2022-10-18
DOI
—
🏛️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)

Some inequalities for these functions are expressed.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, the Hermite-Hadamard inequality for $p-$convex function is provided.
📊
Key Findings & Data:Some integral inequalities for them are also presented.
💡
Conclusion & Impact:Some inequalities for these functions are expressed.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables: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.

🔖

Cite This Article

Eken, Z., Adilov, G., Kemali, S., Tınaztepe, G. (2022). The Hermite-Hadamard inequalities for $p$-convex functions. Hacettepe Journal of Mathematics and Statistics, Cilt: 50 - Sayı: 5, 1268–1279. https://ajindex.com/articles/529453

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (17)

  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 [4] G. Birkhoff and M.K. Bennett, The convexity lattice of a poset, Order 2 (3), 223–242, 1985
  4. 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
  5. S.S. Dragomir, Inequalities of Hermite-Hadamard type for GG-convex functions, Indian J. Math. 60 (1), 1–21, 2018
  6. S.S. Dragomir, Inequalities of Hermite-Hadamard type for GH-convex functions, Electron. J. Math. Anal. Appl. 7 (2), 244–255, 2019
  7. 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
  8. S.S. Dragomir and C. Pearce, Selected topics on Hermite-Hadamard inequalities and applications, RGMIA Monographs, Victoria University, 2000
  9. 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
  10. S.S. Dragomir and S. Fitzpatrick, The Hadamard inequalities for s-convex functions in the second sense. Demonstr. Math. 32 (4), 687–696, 1999
  11. X.C. Huang and X.P. Zhou, Probabilistic assessment for slope using the generalized Chebyshev inequalities, Int. J. Geomec. 20 (4), 06020003, 2020
  12. I. Kawai, Locally convex lattices, J. Math. Soc. Jpn. 9 (3), 281–314, 1957
  13. 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
  14. S. Kemali, I. Yesilce and G. Adilov, $B$-Convexity, $B^{-1}$-Convexity, and Their Comparison, Numer. Func. Anal. Opt. 36 (2), 133–146, 2015
  15. 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
  16. S. Nayak, The Hadamard determinant inequality-Extensions to operators on a Hilbert space, J. Func. Analysis 274 (10), 2978–3002, 2018
  17. H. Ogasawara, The multivariate Markov and multiple