Hermite-Hadamard Type Inequalities for m-Convex and (α, m)-Convex Stochastic Processes

Article Sidebar

PDF
Cite as:
Serap Ozcan, Hermite-Hadamard Type Inequalities for m-Convex and (α, m)-Convex Stochastic Processes, Int. J. Anal. Appl., 17 (5) (2019), 793-802.

Main Article Content

Serap Ozcan

Abstract

In this paper, the concepts of m-convex and (α, m)-convex stochastic processes are introduced. Several new inequalities of Hermite-Hadamard type for differentiable m-convex and (α, m)-convex stochastic processes are established. The results obtained in this work are the generalizations of the known results.

Article Details

References

  1. M. K. Bakula, M. E. Ozdemir and J. Pecaric, Hadamard type inequalities for ¨ m-convex and (α, m)-convex functions, J. Inequal. Pure Appl. Math., 9(4) (2008), Article 96.
  2. M. K. Bakula, J. Pecaric and M. Ribicic, Companion inequalities to Jensen's inequality for m-convex and (α, m)-convex functions, J. Inequal. Pure Appl. Math., 7(5) (2006), Article 194.
  3. S. S. Dragomir and R. P. Agarwal, Two inequalities for differentiable mappings and applications to special means of real numbers and trapezoidal formula, Appl. Math. Lett., 11(5) (1998), 91-95.
  4. L. Gonzalez, N. Merentes and M. Valera-Lopez, Some estimates on the Hermite-Hadamard inequality through convex and quasi-convex stochastic processes, Math. Eterna, 5(5) (2015), 745-767.
  5. I. I ¸scan, H. Kadakal and M. Kadakal, Some new integral inequalities for functions whose nth derivatives in absolute value are (α, m)-convex functions, New Trends Math. Sci., 5(2) (2017), 180-185.
  6. D. Kotrys, Hermite-Hadamard inequality for convex stochastic processes, Aequationes Math., 83 (2012), 143-151.
  7. D. Kotrys, Remarks on strongly convex stochastic processes, Aequationes Math., 86 (2013), 91-98.
  8. L. Li and Z. Hao, On Hermite-Hadamard inequality for h-convex stochastic processes, Aequationes Math., 91 (2017), 909-920.
  9. V. G. Mihe ¸san, A generalization of the convexity, Seminer on Functional Equations, Approximation and Convexity, ClujNapoca, Romania, 1993.
  10. K. Nikodem, On convex stochastic processes, Aequationes Math., 20 (1980), 184-197.
  11. N. Okur, I. I ¸scan and E. Yuksek Dizdar, Hermite-Hadamard type inequalities for p-convex stochastic processes, Int. J. Optim. Control, Theor. Appl., 9(2) (2019), 148-153.
  12. M. Z. Sarikaya, H. Yaldiz and H. Budak, Some integral inequalities for convex stochastic processes, Acta Math. Univ. Comenianae, 85 (2016), 155-164.
  13. E. Set, M Sardari, M. E. Ozdemir and J. Rooin, On generalizations of the Hadamard inequality for ( ¨ α, m)-convex functions, Kyungpook Math. J., 52 (2012), 307-317.
  14. E. Set, M. Tomar and S. Maden, Hermite-Hadamard type inequalities for s-convex stochastic processes in the second sense, Turk. J. Anal. Numb. Theory, 2(6) (2016), 202-207.
  15. E. Set, M. Z. Sarikaya and M. Tomar, Hermite-Hadamard type inequalities for coordinates convex stochastic processes, Math. Aeterna, 5(2) (2015), 363-382.
  16. M. Shaked and J. G. Shanthikumar, Stochastic convexity and its applications, Adv. Appl. Probab., 20 (1988), 427-446.
  17. A. Skowronski, On some properties of J-convex stochastic processes, Aequationes Math., 44 (1992), 249-258.
  18. G. Toader, Some generalizations of the convexity, Proc. Colloq. Approx. Optim., Univ. Cluj-Napoca, Cluj-Napoca, Romania, (1985), 329-338.
  19. M. Tomar, E. Set and S. Maden, Hermite-Hadamard type inequalities for log-convex stochastic processes, J. New Theory, 2 (2015), 23-32.