Research Article
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On Preinvexity For Stochastic Processes

Year 2014, Volume: 7 Issue: 1, 15 - 22, 31.01.2014
https://izlik.org/JA54UN32YD

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.

References

  • Ben-Israel, A. and Mond, B. (1986). What is invexity?. Journal of the Australian Mathematical Society, 28(1), 1-9.
  • 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.
  • 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.
  • Denuit, M. (2000). Time stochastic s-convexity of claim processes. Insurance Mathematics and Economics, 26(2-3), 203-211.
  • Hanson, M.A. (1981). On sufficiency of the Kuhn-Tucker conditions. Journal of Mathematical Analysis and Applications, 80(2), 545-550.
  • Kotrys, D. (2012). Hermite{Hadamard inequality for convex stochastic processes. Aequationes Mathematicae, 83, 143-151.
  • Kotrys, D. (2013). Remarks on strongly convex stochastic processes. Aequationes Mathematicae, 86, 91-98.
  • Mishra, S.K. and Giorgi, G. (2008). Invexity and optimization. Nonconvex optimization and Its Applications, 88, Springer-Verlag, Berlin.
  • Mohan, S.R. and Neogy, S.K. (1995). On invex sets and preinvex functions. Journal of Mathematical Analysis and Applications, 189(3), 901-908.
  • Nikodem, K. (1980). On convex stochastic processes. Aequationes Mathematicae, 20, 184-197.
  • Noor, M.A. (2007). On Hadamard integral inequalities involving two log-preinvex functions. Journal of Inequalities in Pure and Applied Mathematics, 8(3), 1-6.
  • Shaked, M. and Shanthikumar, J.G. (1988). Stochastic Convexity and its Applications. Advances in Applied Probability, 20, 427-446.
  • Shaked, M. and Shanthikumar, J.G. (1988). Temporal Stochastic Convexity and Concavity. Stochastic Processes and Their Applications, 27, 1-20.
  • Shanthikumar, J.G. and Yao, D.D. (1992). Spatiotemporal Convexity of Stochastic Processes and Applications. Probability in the Engineering and Informational Sciences, 6, 1-16.
  • Shynk, J.J. (2013). Probability, Random Variables, and Random Processes: Theory and Signal Processing Applications. Wiley.
  • Skowronski, A. (1992). On some properties of J-convex stochastic processes. Aequationes Mathematicae, 44, 249-258.
  • Skowronski, A. (1995). On Wright-convex stochastic processes. Annales Mathematicae Silesianae, 9, 29-32.

Year 2014, Volume: 7 Issue: 1, 15 - 22, 31.01.2014
https://izlik.org/JA54UN32YD

Abstract

References

  • Ben-Israel, A. and Mond, B. (1986). What is invexity?. Journal of the Australian Mathematical Society, 28(1), 1-9.
  • 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.
  • 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.
  • Denuit, M. (2000). Time stochastic s-convexity of claim processes. Insurance Mathematics and Economics, 26(2-3), 203-211.
  • Hanson, M.A. (1981). On sufficiency of the Kuhn-Tucker conditions. Journal of Mathematical Analysis and Applications, 80(2), 545-550.
  • Kotrys, D. (2012). Hermite{Hadamard inequality for convex stochastic processes. Aequationes Mathematicae, 83, 143-151.
  • Kotrys, D. (2013). Remarks on strongly convex stochastic processes. Aequationes Mathematicae, 86, 91-98.
  • Mishra, S.K. and Giorgi, G. (2008). Invexity and optimization. Nonconvex optimization and Its Applications, 88, Springer-Verlag, Berlin.
  • Mohan, S.R. and Neogy, S.K. (1995). On invex sets and preinvex functions. Journal of Mathematical Analysis and Applications, 189(3), 901-908.
  • Nikodem, K. (1980). On convex stochastic processes. Aequationes Mathematicae, 20, 184-197.
  • Noor, M.A. (2007). On Hadamard integral inequalities involving two log-preinvex functions. Journal of Inequalities in Pure and Applied Mathematics, 8(3), 1-6.
  • Shaked, M. and Shanthikumar, J.G. (1988). Stochastic Convexity and its Applications. Advances in Applied Probability, 20, 427-446.
  • Shaked, M. and Shanthikumar, J.G. (1988). Temporal Stochastic Convexity and Concavity. Stochastic Processes and Their Applications, 27, 1-20.
  • Shanthikumar, J.G. and Yao, D.D. (1992). Spatiotemporal Convexity of Stochastic Processes and Applications. Probability in the Engineering and Informational Sciences, 6, 1-16.
  • Shynk, J.J. (2013). Probability, Random Variables, and Random Processes: Theory and Signal Processing Applications. Wiley.
  • Skowronski, A. (1992). On some properties of J-convex stochastic processes. Aequationes Mathematicae, 44, 249-258.
  • Skowronski, A. (1995). On Wright-convex stochastic processes. Annales Mathematicae Silesianae, 9, 29-32.
There are 17 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Hande Gunay Akdemir

Nurgul Okur Bekar

İmdat Iscan

Publication Date January 31, 2014
IZ https://izlik.org/JA54UN32YD
Published in Issue Year 2014 Volume: 7 Issue: 1

Cite

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