Journals / An International Journal of Optimization and Control: Theories & Applications (IJOCTA) / 2019 / Cilt: 9 - Sayı: 2

On Hermite-Hadamard type inequalities for S φ −preinvex functions by using Riemann-Liouville fractional integrals

Pages
253–260
Publication Date
2022-10-11
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)

These inequalities are a generalization of someof the results in the literature.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, we have obtained some Hermite-Hadamard type integral inequal-ities for s φ −preinvex functions.
📊
Key Findings & Data:In this study, we have obtained some Hermite-Hadamard type integral inequal-ities for s φ −preinvex functions.
💡
Conclusion & Impact:These inequalities are a generalization of someof the results in the literature.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this study, we have obtained some Hermite-Hadamard type integral inequal-ities for s φ −preinvex functions. These inequalities are a generalization of someof the results in the literature.

🔖

Cite This Article

YILDIRIM, H., AKKURT, A., KILINÇ, S. (2022). On Hermite-Hadamard type inequalities for S φ −preinvex functions by using Riemann-Liouville fractional integrals. An International Journal of Optimization and Control: Theories & Applications (IJOCTA), Cilt: 9 - Sayı: 2, 253–260. https://ajindex.com/articles/440590

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (7)

  1. Katugampola, U. N. (2011). New Approach to a generalized fractional integral. Applied Mathematics and Computation, 218(3), 860- 865. Kilbas, A., Srivastava, H. M. and Trujillo, J.J. (2006). Theory and applications of fractional differantial equations. Elsevier B.V., Amster- dam Netherlands. Samko, S. G., Kilbas, A. A. and Marichev, O. I. (1993). Fractional Integral and Deriva- tives, Theory and Applications. Gordon and Breach, Yverdon et alibi. Ozdemir, M. E., Yildiz, C. and Kavur- maci, H. (2015). Fractional integral inequal- ities for different functions. New Trends in Mathematical Sciences, 3(2)2, 110-117.
  2. Sarikaya, M. Z., Set, E., Yaldiz, H. and Basak, N. (2013). Hermite-Hadamard’s. in- equalities for fractional integrals and re- lated fractional inequalities. Mathematical and Computer Modelling 57, 2403-2407.
  3. Wang, J., Li, X., Feckan, M. and Zhou, Y. (2012). Hermite-Hadamard type inequalities for Riemann-Liouville fractional integrals via two kinds of convexity. Applicable Analysis, doi:10.1080/00036811.2012.727986. Yıldırım, H. and Kırtay, Z. (2014). Ostrowski Inequality for Generalized Fractional Integral and Related Inequalities. Malaya Journal of Mathematics, 2(3) 322-329.
  4. Das, S. (2011). Functional Fractional Calcu- lus. Springer-Verlag, Berlin Heidelberg. Sarikaya, M. Z., Dahmani, Z., Kiris, M. and Ahmad, F. (2016). (k, s)−Riemann-Liouville fractional integral and applications. Hacettepe Journal of Mathematics and Statistics, 45(1), 77 – 89. Akkurt, A. and Yıldırım, H. (2013). On Feng Qi type integral inequalities for gener- alized fractional integrals. International Ana- tolia Academic Online Journal, Scientific Sci- ence, 1(2), 22-25.
  5. Noor, M. A. and Awan, M. U. (2013). Some Integral inequalities for two kinds of convex- ities via fractional integrals. Transylvanian Journal of Mathematics and Mechanics, 5(2), 129-136.
  6. Cristescu, G. (2004). Hadamard type in- equalities for φ−convex functions, Annals of the University of Oradea, Fascicle of Man- agement and Technological Engineering, CD- Rom Edition, III (XIII). Dragomir, S. S. and Pearce, C. E. M. (2000). Selected topics on Hermite-Hadamard in- equalities and applications, Victoria Univer- sity, Australia. Dragomir, S. S., Pećarić, J. and Persson, L. E. (1995). Some inequalities of Hadamard type. Soochow Journal of Mathematics, 21, 335-341.
  7. Cristescu, G. (2005). Improved integral in- equalities for products of convex functions. Journal of Inequalities in Pure and Applied Mathematics, 6(2). Zhan