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Year 2019, Volume: 7 Issue: 2, 352 - 358, 15.10.2019

Abstract

References

  • [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 Calculus, AIP Publishing: AIP Conf Proc 1833 020043(2017), 1–4.
  • [19] S. S. Dragomir, J. Pe˘cari´c, L. E. Persson, Some inequalities of Hadamard type, Soochow J. Math., 21(1995), 335–341.
  • [20] T. Y. Zhang, A. P. Ji, F. Qi, On Integral Inequalities of Hermite-Hadamard Type Inequalities for s-Geometrically Convex Functions, Abstr. Appl. Anal., doi:10.11 55/2012/560586.
  • [21] S. Turhan, ˙I. ˙Is¸can, M. Kunt, Hermite-Hadamard Type Inequalities for MjA convex functions, https://doi.org/10.13140/rg.2.2.14526.28486
  • [22] ˙I. ˙Is¸can, Hermite-Hadamard Type Inequalities for harmonically convex functions, Hacet. J. Math. Stat., 43(2014), 6, 935–942.

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

Year 2019, Volume: 7 Issue: 2, 352 - 358, 15.10.2019

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.

References

  • [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 Calculus, AIP Publishing: AIP Conf Proc 1833 020043(2017), 1–4.
  • [19] S. S. Dragomir, J. Pe˘cari´c, L. E. Persson, Some inequalities of Hadamard type, Soochow J. Math., 21(1995), 335–341.
  • [20] T. Y. Zhang, A. P. Ji, F. Qi, On Integral Inequalities of Hermite-Hadamard Type Inequalities for s-Geometrically Convex Functions, Abstr. Appl. Anal., doi:10.11 55/2012/560586.
  • [21] S. Turhan, ˙I. ˙Is¸can, M. Kunt, Hermite-Hadamard Type Inequalities for MjA convex functions, https://doi.org/10.13140/rg.2.2.14526.28486
  • [22] ˙I. ˙Is¸can, Hermite-Hadamard Type Inequalities for harmonically convex functions, Hacet. J. Math. Stat., 43(2014), 6, 935–942.
There are 22 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Erdal Ünlüyol

Seren Salaş This is me

Publication Date October 15, 2019
Submission Date January 25, 2019
Acceptance Date July 30, 2019
Published in Issue Year 2019 Volume: 7 Issue: 2

Cite

APA Ünlüyol, E., & Salaş, S. (2019). Convexity and Hermite-Hadamard Type Inequality via Non-Newtonian Calculus. Konuralp Journal of Mathematics, 7(2), 352-358.
AMA Ünlüyol E, Salaş S. Convexity and Hermite-Hadamard Type Inequality via Non-Newtonian Calculus. Konuralp J. Math. October 2019;7(2):352-358.
Chicago Ünlüyol, Erdal, and Seren Salaş. “Convexity and Hermite-Hadamard Type Inequality via Non-Newtonian Calculus”. Konuralp Journal of Mathematics 7, no. 2 (October 2019): 352-58.
EndNote Ünlüyol E, Salaş S (October 1, 2019) Convexity and Hermite-Hadamard Type Inequality via Non-Newtonian Calculus. Konuralp Journal of Mathematics 7 2 352–358.
IEEE E. Ünlüyol and S. Salaş, “Convexity and Hermite-Hadamard Type Inequality via Non-Newtonian Calculus”, Konuralp J. Math., vol. 7, no. 2, pp. 352–358, 2019.
ISNAD Ünlüyol, Erdal - Salaş, Seren. “Convexity and Hermite-Hadamard Type Inequality via Non-Newtonian Calculus”. Konuralp Journal of Mathematics 7/2 (October 2019), 352-358.
JAMA Ünlüyol E, Salaş S. Convexity and Hermite-Hadamard Type Inequality via Non-Newtonian Calculus. Konuralp J. Math. 2019;7:352–358.
MLA Ünlüyol, Erdal and Seren Salaş. “Convexity and Hermite-Hadamard Type Inequality via Non-Newtonian Calculus”. Konuralp Journal of Mathematics, vol. 7, no. 2, 2019, pp. 352-8.
Vancouver Ünlüyol E, Salaş S. Convexity and Hermite-Hadamard Type Inequality via Non-Newtonian Calculus. Konuralp J. Math. 2019;7(2):352-8.
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