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Dergiler / Turkish Journal of Mathematics and Computer Science / 2021 / Cilt: 13 - Sayı: 2

Hermite-Hadamard Type Inequalities Related to s-Convex Functions in the Third Sense

Zeynep EKEN
Sayfa
318–330
Yayın Tarihi
2022-11-02
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

In addition, these inequalities are used to find an upper bound for error in numerical integration for this type offunctions.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In this paper, some Hermite-Hadamardtype inequalitesfor $s$-convex functions in the third sense are studied.
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Temel Bulgular & Veri:It is establishedseveral new inequalities for functions whose derivative in absolute value and $p$th power of its derivative in absolute valueare $s$-convex in the third sense.
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Sonuç & Katkı:In addition, these inequalities are used to find an upper bound for error in numerical integration for this type offunctions.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri

Abstract

In this paper, some Hermite-Hadamardtype inequalitesfor $s$-convex functions in the third sense are studied. It is establishedseveral new inequalities for functions whose derivative in absolute value and $p$th power of its derivative in absolute valueare $s$-convex in the third sense. In addition, these inequalities are used to find an upper bound for error in numerical integration for this type offunctions.

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Bu Makaleye Atıf Yap

EKEN, Z. (2022). Hermite-Hadamard Type Inequalities Related to s-Convex Functions in the Third Sense. Turkish Journal of Mathematics and Computer Science, Cilt: 13 - Sayı: 2, 318–330. https://ajindex.com/articles/609076

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Kaynakça (17)

  1. Adilov, G., Yesilce, I., On Generalizations of the Concept of Convexity, Hacettepe Journal of Mathematics and Statistics, 41(2012), 723–730
  2. Adilov, G., Yesilce, I., $B^{-1}$-convex Functions, Journal of Convex Analysis, 24(2017), 505–517
  3. Adilov, G., Yesilce, I., Some important properties of $B$-convex functions, Journal of Nonlinear and Convex Analysis, 19(2018), 669-680
  4. Adilov, G. R., Kemali, S., Abstract convexity and Hermite-Hadamard type inequalities, Journal of Inequalities and Applications, 2009(2009), 943534
  5. Alomari, M.W., Darus, M., Kirmaci, U.S., Some inequalities of Hermite-Hadamard type for s-convex functions, Acta Mathematica Scientia, 31(2011), 1643–1652
  6. Avriel, M., r-convex Functions, Mathematical Programming, 2(1972), 309–323
  7. Bayoumi, A., Fathy Ahmed A., p-Convex Functions in Discrete Sets, International Journal of Engineering and Applied Sciences, 4(2017), 63–66
  8. Breckner, W.W., Stetigkeitsaussagen füreine Klasse verallgemekterter konvexer Funktionen in topologischen linearen Raumen, Publ. Inst. Math., 23(1978), 13–20
  9. Briec W., Horvath, C., B-convexity, Optimization, 53(2004), 103–127
  10. Dragomir, S., Fitzpatrick, S., Hadamard’s inequality for s-convex functions in the first sense and applications, Demonstratio Mathematica, 31(1998), 633–642
  11. Dragomir, S. S., Fitzpatrick, S., The Hadamard inequalities for s-convex functions in the second sense, Demonstratio Mathematica, 32(1999), 687–696
  12. Eken, Z., Kemali, S., Tinaztepe, G., Adilov G., The Hermite-Hadamard Inequalities for p-Convex Functions, Hacettepe Journal of Mathematics and Statistics, 50(5)(2021), 1268–1279,
  13. Gozpinar, A., Set, E., Dragomir, S S., Some generalized Hermite-Hadamard type inequalities involving fractional integral operator for functions whose second derivatives in absolute value are s-convex, Acta Mathematica Universitatis Comenianae, 88(2019), 87–100
  14. Kemali, S., Sezer, S., Tinaztepe, G., Adilov, G., s-Convex Functions in the Third Sense, Korean J. Math., 29(3)(2021), 593–602
  15. Kemali, S., Tinaztepe, G., Adilov, G., New Type Inequalities For B-Convex Functions Involving Hadamard Fractional Integral, Facta Universitatis-Series Mathematics And Informatics, 33(2018), 697–704
  16. Orlicz, W., A note on modular spaces I, Bull. Acad. Polon. Soi., Ser. Math. Astronom Phys., 9(1961), 157-162
  17. Özcan, S., Iscan, I., Some new Hermite-Hadamard type inequalities for s-co