Research Article

ON SOME NEW HADAMARD TYPE INEQUALITIES FOR $(s, r)$-PREINVEX FUNCTIONS IN THE SECOND SENSE

Volume: 5 Number: 1 April 1, 2017
EN

ON SOME NEW HADAMARD TYPE INEQUALITIES FOR $(s, r)$-PREINVEX FUNCTIONS IN THE SECOND SENSE

Abstract

In this paper the authors introduce a new class of preinvexity called $(s, r)$-preinvex functions in the second sense and establish some new Hadamard-type inequalities.

Keywords

References

  1. 1] A.O. Akdemir and M. Tunc, On some integral inequalities for s-logarithmically convex functions and their applications, arXiv: 1212.1584v1[math.FA] 7 Dec 2012.
  2. [2] T. Antczak, r-preinvexity and r-invexity in mathematical programming. Comput. Math. Appl. 50 (2005), no. 3-4, 551{566.
  3. [3] M. Avriel, r-convex functions. Math. Programming 2 (1972), 309-323.
  4. [4] R. F. Bai, F. Qi, and B. Y. Xi, Hermite-Hadamard type inequalities for the m- and (alpha,m)- logarithmically convex functions. Filomat 27 (2013), no. 1, 1-7.
  5. [5] A. Barani, A.G. Ghazanfari and S. S. Dragomir, Hermite-Hadamard inequality for functions whose derivatives absolute values are preinvex, RGMIA Research Report Collection, 14 (2011), Article 64, 11 pp.
  6. [6] A. Barani, A. G. Ghazanfari and S. S. Dragomir, Hermite-Hadamard inequality through prequasi invex functions, RGMIA Research Report Collection, 14 (2011), Article 48, 7 pp.
  7. [7] A. Ben-Israel and B. Mond, What is invexity? J. Austral. Math. Soc. Ser. B 28 (1986), no. 1, 1-9.
  8. [8] W. W. Breckner, Stetigkeitsaussagen fur eine Klasse verallgemeinerter konvexer Funktionen in topologischen linearen Raumen. (German) Publ. Inst. Math. (Beograd) (N.S.) 23(37) (1978), 13-20.

Details

Primary Language

English

Subjects

Engineering

Journal Section

Research Article

Authors

B. Meftah
University of 8 Mai 1945 Guelma
Algeria

K. Boukerrıoua
University of Badji-Mokhtar
Algeria

T. Chıheb This is me
University of 8 Mai 1945 Guelma
Algeria

Publication Date

April 1, 2017

Submission Date

February 15, 2017

Acceptance Date

November 16, 2016

Published in Issue

Year 2017 Volume: 5 Number: 1

APA
Meftah, B., Boukerrıoua, K., & Chıheb, T. (2017). ON SOME NEW HADAMARD TYPE INEQUALITIES FOR $(s, r)$-PREINVEX FUNCTIONS IN THE SECOND SENSE. Konuralp Journal of Mathematics, 5(1), 24-42. https://izlik.org/JA99GH96WF
AMA
1.Meftah B, Boukerrıoua K, Chıheb T. ON SOME NEW HADAMARD TYPE INEQUALITIES FOR $(s, r)$-PREINVEX FUNCTIONS IN THE SECOND SENSE. Konuralp J. Math. 2017;5(1):24-42. https://izlik.org/JA99GH96WF
Chicago
Meftah, B., K. Boukerrıoua, and T. Chıheb. 2017. “ON SOME NEW HADAMARD TYPE INEQUALITIES FOR $(s, R)$-PREINVEX FUNCTIONS IN THE SECOND SENSE”. Konuralp Journal of Mathematics 5 (1): 24-42. https://izlik.org/JA99GH96WF.
EndNote
Meftah B, Boukerrıoua K, Chıheb T (April 1, 2017) ON SOME NEW HADAMARD TYPE INEQUALITIES FOR $(s, r)$-PREINVEX FUNCTIONS IN THE SECOND SENSE. Konuralp Journal of Mathematics 5 1 24–42.
IEEE
[1]B. Meftah, K. Boukerrıoua, and T. Chıheb, “ON SOME NEW HADAMARD TYPE INEQUALITIES FOR $(s, r)$-PREINVEX FUNCTIONS IN THE SECOND SENSE”, Konuralp J. Math., vol. 5, no. 1, pp. 24–42, Apr. 2017, [Online]. Available: https://izlik.org/JA99GH96WF
ISNAD
Meftah, B. - Boukerrıoua, K. - Chıheb, T. “ON SOME NEW HADAMARD TYPE INEQUALITIES FOR $(s, R)$-PREINVEX FUNCTIONS IN THE SECOND SENSE”. Konuralp Journal of Mathematics 5/1 (April 1, 2017): 24-42. https://izlik.org/JA99GH96WF.
JAMA
1.Meftah B, Boukerrıoua K, Chıheb T. ON SOME NEW HADAMARD TYPE INEQUALITIES FOR $(s, r)$-PREINVEX FUNCTIONS IN THE SECOND SENSE. Konuralp J. Math. 2017;5:24–42.
MLA
Meftah, B., et al. “ON SOME NEW HADAMARD TYPE INEQUALITIES FOR $(s, R)$-PREINVEX FUNCTIONS IN THE SECOND SENSE”. Konuralp Journal of Mathematics, vol. 5, no. 1, Apr. 2017, pp. 24-42, https://izlik.org/JA99GH96WF.
Vancouver
1.B. Meftah, K. Boukerrıoua, T. Chıheb. ON SOME NEW HADAMARD TYPE INEQUALITIES FOR $(s, r)$-PREINVEX FUNCTIONS IN THE SECOND SENSE. Konuralp J. Math. [Internet]. 2017 Apr. 1;5(1):24-42. Available from: https://izlik.org/JA99GH96WF
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