SavedAdd your journal

Journals / Konuralp Journal of Mathematics / 2019 / Cilt: 7 - Sayı: 2

Convexity and Hermite-Hadamard Type Inequality via Non-Newtonian Calculus

Erdal ÜNLÜYOL
Seren SALAŞ
Pages
352–358
Publication Date
2019-10-15
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)

Finally, we reveal the new generalization of the definition of convexity that can reduce many order of convexity and constitute some new Hermite-Hadamard type inequalities for this calculi.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, firstly we research basic definition of convexity in terms of non-Newtonian calculi, i.e. interval, convex set, convexity, etc.
📊
Key Findings & Data:Secondly, we deal with the different classes of convexity and generalizations via non-Newtonian calculi.
💡
Conclusion & Impact:Finally, we reveal the new generalization of the definition of convexity that can reduce many order of convexity and constitute some new Hermite-Hadamard type inequalities for this calculi.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Non-Newtonian calculi · alpha-convexity · Hermite-Hadamard type inequality

Abstract

In this paper, firstly we research basic definition of convexity in terms of non-Newtonian calculi, i.e. interval, convex set, convexity, etc. Secondly, we deal with the different classes of convexity and generalizations via non-Newtonian calculi. Finally, we reveal the new generalization of the definition of convexity that can reduce many order of convexity and constitute some new Hermite-Hadamard type inequalities for this calculi.

🔖

Cite This Article

ÜNLÜYOL, E., SALAŞ, S. (2019). Convexity and Hermite-Hadamard Type Inequality via Non-Newtonian Calculus. Konuralp Journal of Mathematics, Cilt: 7 - Sayı: 2, 352–358. https://ajindex.com/articles/786494

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (18)

  1. M. Grossman, R. Katz, Non-Newtonian Calculus, Pigeon Cove (1972), Massachusetts, USA: Lee Press
  2. A. E. Bashirov, E. M. Kurpınar, A. O¨ zyapıcı, Multiplicative calculus and its applications, J. Math. Anal. Appl. 337(2008), 36–48
  3. A.E. Bashirov, S. Norozpour, On an alternative view to complex calculus, Math. Methods. Appl. Sci. 41(2018), 7313–7324
  4. C. T¨urkmen, F. Bas¸ar, Some Basic Results on the Sets of Squences with Geometric Calculus, Commun. Fac. Univ. Ank. Series A1 61(2012), 17–34
  5. A. F. C¸ akmak, F. Bas¸ar, Some New Results on Squence Spaces with respect to Non-Newtonian Calculus, J. Inequal. Appl. 228(2012), 1–17
  6. Z. C¸ akır, Spaces of Continuous and Bounded Functions over the Field of Geometric Complex Numbers J. Inequal. Appl. 363(2013), 1–8
  7. U. Kadak, H. Efe, The Contruction of Hilbert Spaces over the Non-Newtonian Field, Int. J. Anal. 2014(2014), 1–10
  8. Y. G¨urefe, U. Kadak, E. Misirli, A. Kurdi, A New Look at the Classical Squence Spaces by Using Multiplicative Calculus, U. P. B. Sci. Bull. Series A 78(2016), 9–20
  9. U. Kadak, Y. G¨urefe, A Generalization on Weighted Means and Convex Functions with respect to the Non-Newtonian Calculus, Int. J. Anal. 2016(2016), 1–9
  10. A. F. C¸ akmak, F. Bas¸ar, Some sequence spaces and matrix transformations in multiplicative sense, TWMS J. Pure Appl. Math. 6 (1) (2015), 27–37
  11. A. F. C¸ akmak, F. Bas¸ar, Certain spaces of functions over the field of non-Newtonian complex numbers, Abstr. Appl. Anal. 2014, Article ID 236124, 12 pages, 2014. doi:10.1155/2014/236124
  12. A. F. C¸ akmak, F. Bas¸ar, On line and double integrals in the non-Newtonian sense, AIP Conference Proceedings, 1611 (2014), 415–423
  13. S. Tekin, F. Bas¸ar, Certain sequence spaces over the non-Newtonian complex field, Abstr. Appl. Anal. 2013, Article ID 739319, 11 pages, doi: 10.1155/2013/ 739319
  14. C. T¨urkmen, F. Basar, Some basic results on the sets of sequences with geometric calculus, AIP Conference Proceedings 1470 (2012), 95–98
  15. K. Boruah, B. Hazarika, Application of Geometric Calculus in Numerical Analysis and difference sequence spaces, J. Math. Anal. Appl. 449(2)(2017), 1265–1285
  16. K. Boruah, B. Hazarika, G-Calculus, TWMS J. Appl. Eng. Math. 8(1)(2018), 94–105
  17. K. Boruah, B. Hazarika, Bigeometric integral calculus, TWMS J. Appl. Eng. Math. 8(2)(2018), 374–385
  18. E. Unluyol, S. Salas¸, ˙I. ˙Is¸can, Convex functions and some inequalities in terms of the Non-Newtonian Calculu