Title: Fractional Ostrowski Type Inequalities for Functions Whose First Derivatives Are s-Preinvex in the Second Sense
Author(s): Badreddine Meftah
Pages: 146-154
Cite as:
Badreddine Meftah, Fractional Ostrowski Type Inequalities for Functions Whose First Derivatives Are s-Preinvex in the Second Sense, Int. J. Anal. Appl., 15 (2) (2017), 146-154.

Abstract


In this paper, we establish an fractional identity. Using this new identity we derives some fractional Ostrowski’s inequalities for functions whose first derivatives are s-preinvex in the second sense.

Full Text: PDF

 

References


  1. A. Ben-Israel and B. Mond, What is invexity?, J. Austral. Math. Soc., Ser. B, 28(1986), No. 1, 1-9.

  2. W. W. Breckner, Stetigkeitsaussagen für eine klasse verallgemeinerter konvexer funktionen in topologischen linearen Räumen, Publ. Inst. Math. (Beograd), 23, (1978), 13–20.

  3. M. A. Hanson, On sufficiency of the Kuhn-Tucker conditions, J. Math. Anal. Appl. 80 (1981) 545-550.

  4. Havva Kavurmacı, M. Emin ¨ Ozdemir and Merve Avcı, New Ostrowski type inequalityes for m-convex functions and applications, Hacettepe Journal ofMathematics and Statistics, Volume 40 (2) (2011), 135–145.

  5. ˙ I. ˙ I¸ scan, Ostrowski type inequalities for functions whose derivatives are preinvex. Bulletin of the Iranian Mathemat- ical Society. Vol. 40 (2014), No. 2, pp. 373-386.

  6. A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and applications of fractional differential equations. North-Holland Mathematics Studies, 204. Elsevier Science B.V., Amsterdam, 2006.

  7. U. S. Kirmaci, Inequalities for differentiable mappings and applications to special means of real numbers and to midpoint formula. Appl. Math. Comput. 147 (2004), no. 1, 137–146.

  8. B. Meftah, Some New Ostrwoski’s Inequalities for Functions Whose nth Derivatives are r-Convex. International Journal of Analysis, 2016, 7 pages

  9. B. Meftah, Ostrowski inequalities for functions whose first derivatives are logarithmically preinvex. Chin. J. Math. (N.Y.) 2016, Art. ID 5292603, 10 pp.

  10. D. S. Mitrinovi´ c, J. E. Peˇ cari´ c and A. M. Fink, Classical and new inequalities in analysis. Mathematics and its Applications (East European Series), 61. Kluwer Academic Publishers Group, Dordrecht, 1993.

  11. M. A. Noor, Variational-like inequalities, Optimization, 30 (1994), 323-330.

  12. M. A. Noor, Invex equilibrium problems, J. Math. Anal. Appl., 302 (2005), 463-475.

  13. M. E. ¨ Ozdemir, H. Kavurmaci, E. Set, Ostrowski’s type inequalities for (α,m)-convex functions, Kyungpook Math. J., 50(2010), 371-378.

  14. J. Peˇ cari´ c, F. Proschan and Y. L. Tong, Convex functions, partial orderings, and statistical applications. Mathe- matics in Science and Engineering, 187. Academic Press, Inc., Boston, MA, 1992.

  15. R. Pini, Invexity and generalized Convexity, Optimization 22 (1991) 513-525.

  16. M. Z. Sarikaya, On the Ostrowski type integral inequality. Acta Math. Univ. Comenian. (N.S.) 79 (2010), no. 1, 129–134.

  17. E. Set, M. E. ¨ Ozdemir and M. Z. Sarıkaya, New inequalities of Ostrowski’s type for s-convex functions in the second sense with applications. Facta Univ. Ser. Math. Inform. 27 (2012), no. 1, 67–82.

  18. Y. Wang, B. -Y. Xi and F. Qi, Hermite-Hadamard type integral inequalities when the power of the absolute value of the first derivative of the integrand is preinvex. Matematiche (Catania) 69 (2014), no. 1, 89–96.

  19. Y. Wang, S-H. Wang and F. Qi, Simpson type integral inequalities in which the power of the absolute value of the first derivative of the integrand is s-preinvex, Facta Univ. Ser. Math. Inform. 28 (2) (2013), 151–159.

  20. T. Weir and B. Mond, (1988). Pre-invex functions in multiple objective optimization, J. Math. Anal.Appl. 136, 29-38.

  21. X. -M. Yang and D. Li, (2001). On properties of preinvex functions, J. Math. Anal. Appl. 256,229-241.