KaydedilenlerDerginizi ekleyin

Dergiler / Turkish Journal of Science / 2023 / Cilt: 8 Sayı: 1

New General Inequalities For Exponential Type Convex Function

Çetin Yıldız(ATATURK UNIVERSITY)0000-0002-8302-343X
Emre Bakan(ATATURK UNIVERSITY)0000-0002-6881-5711
Hüseyin Dönmez(ATATURK UNIVERSITY)0000-0002-6799-1270
Sayfa
11–18
Yayın Tarihi
2023-05-03
DOI
—
🏛️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)

We use these Riemann-Liouville fractional integrals to establish a new integral inequality for exponential type convex function.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In this paper, we introduce the concept of an exponential type convex function.
📊
Temel Bulgular & Veri:We establish new integral inequalities of the Hermite-Hadamard type by using the Power-Mean and Hölder Inequalities.
💡
Sonuç & Katkı:We use these Riemann-Liouville fractional integrals to establish a new integral inequality for exponential type convex function.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Convex function · Exponential type convexity · Hermite-Hadamard inequalities

Abstract

In this paper, we introduce the concept of an exponential type convex function. We establish new integral inequalities of the Hermite-Hadamard type by using the Power-Mean and Hölder Inequalities. Additionally, we give the Riemann-Liouville fractional integrals definitions. We use these Riemann-Liouville fractional integrals to establish a new integral inequality for exponential type convex function.

🔖

Bu Makaleye Atıf Yap

Yıldız, Ç., Bakan, E., Dönmez, H. (2023). New General Inequalities For Exponential Type Convex Function. Turkish Journal of Science, Cilt: 8 Sayı: 1, 11–18. https://ajindex.com/articles/938096

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (15)

  1. Alomari M.W., Dragomir S.S. and Kirmaci U.S., Generalizations of the Hermite-Hadamard type inequalities for functions whose derivatives are s-convex, Acta Commen. Uni. Tartu. Math., 17 (2), 2013.
  2. Kadakal M., İşçan İ., Exponential Type Convexity and Some Related Inequalities. Journal of Inequalities and Application,
  3. Özdemir M.E. and Kırmacı U. S. Two new theorem on mappings uniformly continuous and convex with applications to quadrature rules and means, Appl. Math. Comp., 2003, 143: 269--274.
  4. Hadamard J.: Êtude sur les propriêtês des fonctions entiêres en particullier d'une fonction considêrêê par Riemann. J. Math. Pures Appl. 58, 171-215 (1893)
  5. Özdemir, M.E., Bayraktar, B., Butt. S.I. and Akdemir, A.O., Some New Hermite-Hadamard type inequalities Via Non-Conformable Fractional Integrals, Turkish J. Ineq., 5 (2) (2021), 48 --60.
  6. Set, E., Akdemir, A.O., Karaoğlan, A., Abdeljawad, T. and Shatanawi, W., On New Generalizations of Hermite-Hadamard Type Inequalities via Atangana-Baleanu Fractional Integral Operators, Axioms, 10(3)(2021), 223.
  7. Özdemir, M. E., New Refinements of Hadamard Integral inequlaity via k-Fractional Integrals for p-Convex Function, Turkish Jour. Sci., 6 (1)(2021), 1-5.
  8. Ekinci, A., Akdemir, A.O. and Özdemir, M.E., Integral Inequalities for Different Kinds of Convexity via Classical Inequalities, Turkish Jour. Sci, 5 (3)(2020), 305-313.
  9. Ekinci, A., Özdemir, M.E. and Set, E., New Integral Inequalities of Ostrowski Type for Quasi-Convex Functions with Applications, Turkish Jour. Sci, 5 (3)(2020), 290-304.
  10. Yıldız, Ç., Gürbüz, M. and Akdemir, A.O. The Hadamard Type Inequalities for M- Convex Functions. Konuralp Jour. Math., 1(1)(2013), 40-47.
  11. Chu, Y.M., Khan, M.A., Khan, T.U. and Ali, T., Generalizations of Hermite-Hadamard type inequalities for MT-convex functions, J. Nonlinear Sci. Appl., 9(5)(2016), 4305-4316.
  12. Khan, M.A., Chu, Y., Khan, T.U. and Khan, J., Some new inequalities of Hermite-Hadamard type for s-convex functions with applications, Open Mathematics, 15(1)(2017), 1414-1430.
  13. R. Gorenflo, F. Mainardi, Fractional calculus: integral and differential equations of fractional order, Springer Verlag, Wien (1997), 223-276.
  14. Özdemir, M.E., Dragomir, S.S. and Yıldız, Ç., The Hadamard Inequality For Convex Function Via Fractional Integrals, Acta Math. Sci., 33(5) (2013), 1293-1299.
  15. İşcan, İ., New refinements for integral and sum forms of Hölder inequality, J. Inequal. Appl., 2019:304 (2019).