SavedAdd your journal

Journals / Afyon Kocatepe Üniversitesi Fen ve Mühendislik Bilimleri Dergisi / 2026 / Cilt: 21 Sayı: 4

Some Hermite-Hadamard Type Inequalities for Strongly s-η-Convex Functions

Güçlü s-η-Konveks Fonksiyonlar İçin Bazı Hermite-Hadamard Tipi Eşitsizlikler

Hasan Öğünmez(AFYON KOCATEPE ÜNİVERSİTESİ)0000-0002-2018-317X
Nurila Toigombaeva(AFYON KOCATEPE ÜNİVERSİTESİ)0000-0001-8278-8230
Pages
800–804
Publication Date
2021-08-31
🏛️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)

This article shows new results for this inequality.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this article, the concept of strongly s-η-convex functions, which is a strengthened version of the s-η-convex function, which is one of the generalized convex functions, is introduced.
📊
Key Findings & Data:For strongly s-η-convex functions, Hermite-Hadamard-type inequalities are obtained.
💡
Conclusion & Impact:This article shows new results for this inequality.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:Güçlü s-Konveks · Güçlü η-Konveks · Güçlü s-η-Konveks

Abstract

In this article, the concept of strongly s-η-convex functions, which is a strengthened version of the s-η-convex function, which is one of the generalized convex functions, is introduced. For strongly s-η-convex functions, Hermite-Hadamard-type inequalities are obtained. In addition, with the help of such functions, the difference between the middle and right terms in the Hermite-Hadamard-Fejer inequality for differentiable maps is estimated, and the Hermite-Hadamard-Fejer type inequality is obtained. This article shows new results for this inequality.

Özet

Bu makalede genelleştirilmiş konveks fonksiyonlardan biri olan s-η-konveks fonksiyonunun güçlendirilmiş hali olan, güçlü s-η-konveks fonksiyonlar kavramı tanıtılmaktadır. Güçlü s-η-konveks fonksiyonlar için Hermite-Hadamard tipi eşitsizlikler elde edilmektedir. Ayrıca bu tür fonksiyonlar yardımıyla türevlenebilir dönüşümler için Hermite-Hadamard-Fejer eşitsizliğinde orta ve sağ terimler arasındaki fark tahmin edilerek, Hermite-Hadamard-Fejer tipi eşitsizlik elde edilir. Bu çalışmada bu eşitsizlik için yeni sonuçlar gösterilmektedir.

🔖

Cite This Article

Öğünmez, H., Toigombaeva, N. (2021). Some Hermite-Hadamard Type Inequalities for Strongly s-η-Convex Functions. Afyon Kocatepe Üniversitesi Fen ve Mühendislik Bilimleri Dergisi, Cilt: 21 Sayı: 4, 800–804. https://doi.org/10.35414/akufemubid.946228

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (12)

  1. Awan, M.U., Noor, M.A., Noor, K.I., 2017. Safdar F, On strongly generalized convex functions, Filomat, 31(18), 5783–5790.
  2. Arrow, H.J., Enthowen, A.N.D., 1961. Quasi concave programming. The Econometrica Society, 29(4), 779-800.
  3. Erdem, Y., Öğünmez, H., Budak, H., 2017. On some Hermite-Hadamard type inequalities for strongly s-convex functions. Biska, New Trends in mathematical sciences, 5(3), 154-161.
  4. Gordji, M.E., Dragomir, S.S., Delavar, M.R., 2015. An inequality related to η-convex functions (II). Analysis and Applications, (6)2, 26-32.
  5. Gordji, M.E., Delavar, M.R., Sen, M.D.L., 2016. On φ-convex functions. Journal of mathematical inequalities, 10(1), 173-183.
  6. Gordji, M.E., Delavar, M.R., Dragomir, S.S., 2015. Some inequalities related to η-convex functions. RGMIA, 18(8), 1-14.
  7. Hudziki, H., Maligranda, L., 1994. Some remarks on s-convex functions. Aequationes Mathematicae. 48, 100-111.
  8. Merentes N, Nicodem K, 2010. Remarks on strongly convex functions, Aequationes mathematicae, 80, 193-199.
  9. Ozdemir, M.E., Yıldız, C., Akdemir, A. O., Set, E., 2013. On some inequalities for s-convex functions and applications, Journal of Inequalities and Applications, 2013(333).
  10. Pecaric, J.E., Proschan, F., Tong Y,L., 1992. Convex functions, partial orderings and statistical applications. Academic Press, Boston, 187, 467.
  11. Rangel-Oliveros, Y., Vivas-Cortez, M., 2018. Ostrowski type inequalities for functions whose second derivative are convex generalized. Applied Mathematics and Information Sciences, 12(6), 1055-1064.
  12. Vivas-Cortez, M., Rangel-Oliveros, Y., 2020. An inequality related to s-φ-convex functions. Applied Mathematics Information Sciences, 14(1), 151-154.