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

##### Pages: 793-802

##### 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.#### 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.

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#### References

- 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.
- 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.
- 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.
- 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.
- 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.
- D. Kotrys, Hermite-Hadamard inequality for convex stochastic processes, Aequationes Math., 83 (2012), 143–151.
- D. Kotrys, Remarks on strongly convex stochastic processes, Aequationes Math., 86 (2013), 91–98.
- L. Li and Z. Hao, On Hermite-Hadamard inequality for h-convex stochastic processes, Aequationes Math., 91 (2017), 909–920.
- V. G. Mihe¸san, A generalization of the convexity, Seminer on Functional Equations, Approximation and Convexity, ClujNapoca, Romania, 1993.
- K. Nikodem, On convex stochastic processes, Aequationes Math., 20 (1980), 184–197.
- 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.
- M. Z. Sarıkaya, H. Yaldız and H. Budak, Some integral inequalities for convex stochastic processes, Acta Math. Univ. Comenianae, 85 (2016), 155–164.
- 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.
- 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.
- E. Set, M. Z. Sarıkaya and M. Tomar, Hermite-Hadamard type inequalities for coordinates convex stochastic processes, Math. Aeterna, 5(2) (2015), 363–382.
- M. Shaked and J. G. Shanthikumar, Stochastic convexity and its applications, Adv. Appl. Probab., 20 (1988), 427–446.
- A. Skowronski, On some properties of J-convex stochastic processes, Aequationes Math., 44 (1992), 249–258.
- G. Toader, Some generalizations of the convexity, Proc. Colloq. Approx. Optim., Univ. Cluj-Napoca, Cluj-Napoca, Romania, (1985), 329–338.
- M. Tomar, E. Set and S. Maden, Hermite-Hadamard type inequalities for log-convex stochastic processes, J. New Theory, 2 (2015), 23–32.