Hermite-Hadamard type inequalities for p-convex stochastic processes
Keywords:p-convexity, Stochastic process, Hermite-Hadamard type inequality, Mean-square integralibility
In this study are investigated p-convex stochastic processes which are extensions of convex stochastic processes. A suitable example is also given for this process. In addition, in this case a p-convex stochastic process is increasing or decreasing, the relation with convexity is revealed. The concept of inequality as convexity has an important place in literature, since it provides a broader setting to study the optimization and mathematical programming problems. Therefore, Hermite-Hadamard type inequalities for p-convex stochastic processes and some boundaries for these inequalities are obtained in present study. It is used the concept of mean-square integrability for stochastic processes to obtain the above mentioned results.
Nikodem, K. (1980). On convex stochastic processes. Aequationes Mathematicae, 20, 184-197.
Shaked, M., & Shanthikumar, J.G. (1988). Stochastic convexity and its applications. Advances in Applied Probability, 20, 427-446.
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, 9, 29-32.
Kotrys, D. (2012). Hermite-Hadamard inequality for convex stochastic processes. Aequationes Mathematicae, 83, 143-151.
Akdemir G. H., Okur B. N., Iscan, I. (2014). On Preinvexity for Stochastic Processes. Statistics, Journal of the Turkish Statistical Association, 7 (1), 15-22.
Okur, N., İşcan, İ., Yüksek Dizdar, E. (2018). Hermite-Hadamard Type Inequalities for Harmonically Stochastic Processes, International Journal of Economic and Administrative studies, 11 (18. EYI Special Issue), 281-292.
Tomar, M., Set, E., & Okur B., N. (2014). On Hermite-Hadamard-Type Inequalities for Strongly Log Convex Stochastic Processes. The Journal of Global Engineering Studies, 1(2), 53-61.
İşcan, İ. (2016). Hermite-Hadamard inequalities for p-convex functions. International Journal of Analysis and Applications, 11 (2), 137-145.
Okur B., N., Günay Akdemir, H., & İşcan, İ. (2016). Some Extensions of Preinvexity for Stochastic Processes, G.A. Anastassiou and O. Duman (eds.), Computational Analysis, pp. 259-270, Springer Proceedings in Mathematics & Statistics, Vol. 155, Springer, New York.
Sarikaya, M. Z., Yaldiz, H. & Budak, H. (2016). Some integral inequalities for convex stochastic processes. Acta Mathematica Universitatis Comenianae, 85(1), 155–164.
Fang, Z. B. & Shi, R. (2014). On the (p,h)-convex function and some integral inequalities. Journal of Inequalities and Applications, 2014:45.
Zhang, K. S. & Wan, J. P. (2007). p-convex functions and their properties. Pure and Applied Mathematics, 23(1), 130-133.
Noor, M. A., Noor, K. I., Mihai, M. V. & Awan, M. U. (2016). Hermite-Hadamard ineq. for differentiable p-convex functions using hypergeometric functions. Pub. De L’institut Math. Nouvelle série, tome 100(114), 251–257.
How to Cite
Articles published in IJOCTA are made freely available online immediately upon publication, without subscription barriers to access. All articles published in this journal are licensed under the Creative Commons Attribution 4.0 International License (click here to read the full-text legal code). This broad license was developed to facilitate open access to, and free use of, original works of all types. Applying this standard license to your work will ensure your right to make your work freely and openly available.
Under the Creative Commons Attribution 4.0 International License, authors retain ownership of the copyright for their article, but authors allow anyone to download, reuse, reprint, modify, distribute, and/or copy articles in IJOCTA, so long as the original authors and source are credited.
The readers are free to:
- Share — copy and redistribute the material in any medium or format
- Adapt — remix, transform, and build upon the material
- for any purpose, even commercially.
- The licensor cannot revoke these freedoms as long as you follow the license terms.
under the following terms:
- Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.
This work is licensed under a Creative Commons Attribution 4.0 International License.