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On Preinvexity For Stochastic Processes

Year 2014, Volume: 7 Issue: 1, 15 - 22, 31.01.2014

Hande Gunay Akdemir Nurgul Okur Bekar İmdat Iscan

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

convex stochastic processes mean-square differentiable mean square integral Hermite-Hadamard inequality preinvex functions invex functions

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

Hande Gunay Akdemir Nurgul Okur Bekar İmdat Iscan

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 Articles
Authors

Hande Gunay Akdemir

Nurgul Okur Bekar

İmdat Iscan

Publication Date January 31, 2014
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.
AMA Gunay Akdemir H, Okur Bekar N, Iscan İ. On Preinvexity For Stochastic Processes. IJTSA. January 2014;7(1):15-22.
Chicago Gunay Akdemir, Hande, Nurgul Okur Bekar, and İmdat Iscan. “On Preinvexity For Stochastic Processes”. Istatistik Journal of The Turkish Statistical Association 7, no. 1 (January 2014): 15-22.
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 H. Gunay Akdemir, N. Okur Bekar, and İ. Iscan, “On Preinvexity For Stochastic Processes”, IJTSA, vol. 7, no. 1, pp. 15–22, 2014.
ISNAD Gunay Akdemir, Hande et al. “On Preinvexity For Stochastic Processes”. Istatistik Journal of The Turkish Statistical Association 7/1 (January 2014), 15-22.
JAMA 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, 2014, pp. 15-22.
Vancouver Gunay Akdemir H, Okur Bekar N, Iscan İ. On Preinvexity For Stochastic Processes. IJTSA. 2014;7(1):15-22.
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