THERMAL SCIENCE

International Scientific Journal

Thermal Science - Online First

Authors of this Paper

External Links

online first only

Multidimensional general convexity for stochastic processes and associated with Hermite-Hadamard type integral inequalities

ABSTRACT
In this study, we idetified multidimensional general convex stochastic processes. Concordantly, we obtained some important results related stochastic processes. Moreover, we derived some Hermite-Hadamard type integral inequalities for these stochastic processes.
KEYWORDS
PAPER SUBMITTED: 2019-06-22
PAPER REVISED: 2019-08-15
PAPER ACCEPTED: 2019-08-21
PUBLISHED ONLINE: 2019-10-06
DOI REFERENCE: https://doi.org/10.2298/TSCI190622361O
REFERENCES
  1. Hadamard, J., Étude sur les propriétés des fonctions entières et en particulier d.une function considerée par Riemann, J. Math Pures Appl., 58 (1893), pp. 171-215.
  2. Youness, E.A., E-Convex Sets, E-Convex Functions and E-Convex Programming, J. Optimiz. Theory App., 102 (1999), pp. 439-450.
  3. Sarikaya, M.Z. Büyükeken, M., Kiriş, M.E., On Some Generalized Integral Inequalities For Φ-Convex Functions, Studia Univ. Babeş-Bolyai Mathematica, 60 (2015), 3, pp. 367-377.
  4. Syau, Y. R., Lee, E.S., Some Properties of E-Convex Functions, Appl. Math. Lett., 18 (2005), pp. 1074-1080.
  5. Martinez-Legaz, J.E., Singer, I., On φ-Convexity of Convex Functions, Linear Algebra and its Applications, 278 (1998), pp. 163-181.
  6. Shaikh A.A., Iqbal, A., Mondal, C.K., Some Results on φ-Convex Functions and Geodesic Φ-Convex Functions, Differential Geometry-Dynamical Systems, 20 (2018), pp. 159-169.
  7. Dragomir, S.S., Inequalıtıes of Jensen Type for φ-Convex Functions, Fasciculi Mathematici, 55 (2015), 1, pp.35-52.
  8. Cristescu, G., Hadamard-Type Inequalities for φ-Convex Functions, Annals of the University of Oradea, Fascicle of Man. and Tech. Eng., CD-Rom Edition, 12 (3), 2004.
  9. Set, E., Sarikaya, M.Z., Akdemir, A. O., Hadamard type inequalities for φ-convex functions on the coordinates, Tbilisi Mathematical Journal, 7, (2014), 2, pp.51-60.
  10. De la Cal, J., Carcamo J., Multidimensional Hermite-Hadamard Inequalities and the Convex Order, Journal of Mathematical Analysis and Applications, 324 (2006), pp. 248-261.
  11. Ellahi, H., Farid, G., Rehman, A.U., Hadamard's Inequality for s-Convex Function on n-Coordinates, Proceedings of 1st ICAM Attock, Pakistan, 2015.
  12. Viloria, J.M., Cortez, M.V., Hermite-Hadamard Type Inequalities for Harmonically Convex Functions on ncoordinates, Appl. Math. Inf. Sci. Lett., 6 (2018), 2, pp.1-6.
  13. Nikodem, K., On Convex Stochastic Processes, Aequat. Math., 20 (1980), pp. 184-197.
  14. Shaked, M., Shanthikumar, J.G., Stochastic Convexity and Its Applications, Advances in Applied Probability, 20 (1988), pp.427-446.
  15. Skowronski, A., On Some Properties of J-convex Stochastic Processes, Aequat. Math., 44 (1992), pp. 249-258.
  16. Kotrys, D., Hermite-Hadamard Inequality for Convex Stochastic Processes, Aequat. Math., 83 (2012), pp. 143-151.
  17. Set, E., Sarikaya, M.Z., Tomar, M., Hermite-Hadamard Inequalities for Coordinates Convex Stochastic Processes, Mathematica Aeterna, 5 (2015), 2, pp. 363-382.
  18. Sarikaya, M.Z., Kiriş, M.E., Çelik, N., Hermite-Hadamard Type Inequality for φh-Convex Stochastic Processes, AIP Conference Proceedings 1726, 020076, 2016; doi: 10.1063/1.4945902
  19. Karahan, V., Okur, N., Hermite-Hadamard Type Inequalities for Convex Stochastic Processes On n-Coordinates, Turk. J. Math. Comput. Sci., 10 (2018), pp. 256-262.