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.
References
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Ben-Israel, A. and Mond, B. (1986). What is invexity?. Journal of the Australian Mathematical Society, 28(1), 1-9.
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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.
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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.
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Denuit, M. (2000). Time stochastic s-convexity of claim processes. Insurance Mathematics and Economics, 26(2-3), 203-211.
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Hanson, M.A. (1981). On sufficiency of the Kuhn-Tucker conditions. Journal of Mathematical Analysis and Applications, 80(2), 545-550.
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Kotrys, D. (2012). Hermite{Hadamard inequality for convex stochastic processes. Aequationes Mathematicae, 83, 143-151.
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Kotrys, D. (2013). Remarks on strongly convex stochastic processes. Aequationes Mathematicae, 86, 91-98.
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Mishra, S.K. and Giorgi, G. (2008). Invexity and optimization. Nonconvex optimization and Its Applications, 88, Springer-Verlag, Berlin.
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Mohan, S.R. and Neogy, S.K. (1995). On invex sets and preinvex functions. Journal of Mathematical Analysis and Applications, 189(3), 901-908.
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Nikodem, K. (1980). On convex stochastic processes. Aequationes Mathematicae, 20, 184-197.
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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.
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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.
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Shynk, J.J. (2013). Probability, Random Variables, and Random Processes: Theory and Signal Processing Applications. Wiley.
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Skowronski, A. (1992). On some properties of J-convex stochastic processes. Aequationes Mathematicae, 44, 249-258.
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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
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.