Research Article

On Preinvexity For Stochastic Processes

Volume: 7 Number: 1 January 31, 2014
EN

On Preinvexity For Stochastic Processes

Abstract

In this paper, we introduce preinvex and invex stochastic processes, and we provide related well known Hermite-Hadamard integral inequality for preinvex stochastic processes by considering their left derivative, right derivative, and derivative processes.

Keywords

References

  1. Ben-Israel, A. and Mond, B. (1986). What is invexity?. Journal of the Australian Mathematical Society, 28(1), 1-9.
  2. Chang, C.S., Chao, X. L., Pinedo, M. and Shanthikumar, J.G. (1991). Stochastic convexity for multidimensional processes and its applications. IEEE Transactions on Automatic Control, 36, 1341-1355.
  3. De la Cal, J. and Carcamo, J. (2006). Multidimensional Hermite-Hadamard inequalities and the convex order. Journal of Mathematical Analysis and Applications, 324, 248-261.
  4. Denuit, M. (2000). Time stochastic s-convexity of claim processes. Insurance Mathematics and Economics, 26(2-3), 203-211.
  5. Hanson, M.A. (1981). On sufficiency of the Kuhn-Tucker conditions. Journal of Mathematical Analysis and Applications, 80(2), 545-550.
  6. Kotrys, D. (2012). Hermite{Hadamard inequality for convex stochastic processes. Aequationes Mathematicae, 83, 143-151.
  7. Kotrys, D. (2013). Remarks on strongly convex stochastic processes. Aequationes Mathematicae, 86, 91-98.
  8. Mishra, S.K. and Giorgi, G. (2008). Invexity and optimization. Nonconvex optimization and Its Applications, 88, Springer-Verlag, Berlin.

Details

Primary Language

English

Subjects

-

Journal Section

Research Article

Publication Date

January 31, 2014

Submission Date

September 4, 2014

Acceptance Date

-

Published in Issue

Year 2014 Volume: 7 Number: 1

APA
Gunay Akdemir, H., Okur Bekar, N., & Iscan, İ. (2014). On Preinvexity For Stochastic Processes. Istatistik Journal of The Turkish Statistical Association, 7(1), 15-22. https://izlik.org/JA54UN32YD
AMA
1.Gunay Akdemir H, Okur Bekar N, Iscan İ. On Preinvexity For Stochastic Processes. IJTSA. 2014;7(1):15-22. https://izlik.org/JA54UN32YD
Chicago
Gunay Akdemir, Hande, Nurgul Okur Bekar, and İmdat Iscan. 2014. “On Preinvexity For Stochastic Processes”. Istatistik Journal of The Turkish Statistical Association 7 (1): 15-22. https://izlik.org/JA54UN32YD.
EndNote
Gunay Akdemir H, Okur Bekar N, Iscan İ (January 1, 2014) On Preinvexity For Stochastic Processes. Istatistik Journal of The Turkish Statistical Association 7 1 15–22.
IEEE
[1]H. Gunay Akdemir, N. Okur Bekar, and İ. Iscan, “On Preinvexity For Stochastic Processes”, IJTSA, vol. 7, no. 1, pp. 15–22, Jan. 2014, [Online]. Available: https://izlik.org/JA54UN32YD
ISNAD
Gunay Akdemir, Hande - Okur Bekar, Nurgul - Iscan, İmdat. “On Preinvexity For Stochastic Processes”. Istatistik Journal of The Turkish Statistical Association 7/1 (January 1, 2014): 15-22. https://izlik.org/JA54UN32YD.
JAMA
1.Gunay Akdemir H, Okur Bekar N, Iscan İ. On Preinvexity For Stochastic Processes. IJTSA. 2014;7:15–22.
MLA
Gunay Akdemir, Hande, et al. “On Preinvexity For Stochastic Processes”. Istatistik Journal of The Turkish Statistical Association, vol. 7, no. 1, Jan. 2014, pp. 15-22, https://izlik.org/JA54UN32YD.
Vancouver
1.Hande Gunay Akdemir, Nurgul Okur Bekar, İmdat Iscan. On Preinvexity For Stochastic Processes. IJTSA [Internet]. 2014 Jan. 1;7(1):15-22. Available from: https://izlik.org/JA54UN32YD