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Hermite-Hadamard Type Inequalities for Exponentially p-Convex Stochastic Processes

Yıl 2019, Cilt: 23 Sayı: 5, 1012 - 1018, 01.10.2019

Serap Özcan

https://doi.org/10.16984/saufenbilder.561040
Cited By: 3

Öz

In this paper, the concept of exponentially 𝑝-convex stochastic process is introduced. Several new inequalities of Hermite-Hadamard type for exponentially 𝑝-convex stochastic process are established. Some special cases are given which are obtained from our main results. The results obtained in this work are the generalizations of the known results.

Anahtar Kelimeler

Convex stochastic processes p-convex stochastic processes exponentially p-convex stochastic processes mean-square integral Hermite-Hadamard type inequality

Kaynakça

  • M. Abramovitz and I. A. Stegun, “Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables”, Dover, New York, 1965.
  • L. Gonzalez, N. Merentes and M. Valera-Lopez, “Some estimates on the Hermite-Hadamard inequality through convex and quasi-convex stochastic processes”, Mathematica Aeterna, vol. 5, no. 5, pp. 745–767, 2015.
  • D. Kotrys, “Hermite-Hadamard inequality for convex stochastic processes”, Aequationes Mathematicae, vol. 83, pp. 143–151, 2012.
  • D. Kotrys, “Remarks on strongly convex stochastic processes”, Aequationes Mathematicae, vol. 86, pp. 91–98, 2013.
  • L. Li and Z. Hao, “On Hermite-Hadamard inequality for h-convex stochastic processes”, Aequationes Mathematicae, vol. 91, pp. 909–920, 2017.
  • S. Maden, M. Tomar and E. Set, “Hermite-Hadamard type inequalities for s-convex stochastic processes in first sense”, Pure and Applied Mathematics Letters, vol. 2015, pp. 1–7, 2015.
  • N. Mehreen and M. Anwar, “Hermite-Hadamard type inequalities for exponentially p-convex functions and exponentially s-convex functions in the second sense with applications”, Journal of Inequalities and Applications, vol. 2019, no. 92, pp. 1–17, 2019.
  • K. Nikodem, “On convex stochastic processes”, Aequationes Mathematicae, vol. 20, pp. 184–197, 1980.
  • N. Okur, İ. İşcan and E. Yuksek Dizdar, “Hermite-Hadamard type inequalities for p-convex stochastic processes”, An Int. J. Optim. and Cont., vol. 9, no. 2, pp. 148– 153, 2019.
  • M. Z. Sarıkaya, H. Yaldız and H. Budak, “Some integral inequalities for convex stochastic processes”, Acta Math. Univ. Comenianae, LXXXV, pp. 155–164, 2016.
  • E. Set, M. Tomar and S. Maden, “Hermite-Hadamard type inequalities for s-convex stochastic processes in the second sense”, Turkish Journal of Analysis and Number Theory, vol. 2, no. 6, pp. 202–207, 2016.
  • E. Set, M. Z. Sarıkaya and M. Tomar, “Hermite-Hadamard type inequalities for coordinates convex stochastic processes”, Mathematica Aeterna, vol. 5, no. 2, pp. 363–382, 2015.
  • M. Shaked and J. G. Shanthikumar, “Stochastic convexity and its applications”, Advances in Applied Probability, vol. 20, pp. 427–446, 1988.
  • A. Skowronski, “On some properties of J-convex stochastic processes”, Aequationes Mathematicae, vol. 44, pp. 249–258, 1992.
  • M. Tomar, E. Set and S. Maden, “Hermite-Hadamard type inequalities for log-convex stochastic processes”, Journal of New Theory, vol. 2, pp. 23–32, 2015.
  • M. Tomar, E. Set and N. O. Bekar, “Hermite-Hadamard type inequalities for strongly log-convex stochastic processes”, Journal of Global Engineering Studies, vol. 1, no. 53–61, 2014.

Yıl 2019, Cilt: 23 Sayı: 5, 1012 - 1018, 01.10.2019

Serap Özcan

https://doi.org/10.16984/saufenbilder.561040
Cited By: 3

Öz

Kaynakça

  • M. Abramovitz and I. A. Stegun, “Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables”, Dover, New York, 1965.
  • L. Gonzalez, N. Merentes and M. Valera-Lopez, “Some estimates on the Hermite-Hadamard inequality through convex and quasi-convex stochastic processes”, Mathematica Aeterna, vol. 5, no. 5, pp. 745–767, 2015.
  • D. Kotrys, “Hermite-Hadamard inequality for convex stochastic processes”, Aequationes Mathematicae, vol. 83, pp. 143–151, 2012.
  • D. Kotrys, “Remarks on strongly convex stochastic processes”, Aequationes Mathematicae, vol. 86, pp. 91–98, 2013.
  • L. Li and Z. Hao, “On Hermite-Hadamard inequality for h-convex stochastic processes”, Aequationes Mathematicae, vol. 91, pp. 909–920, 2017.
  • S. Maden, M. Tomar and E. Set, “Hermite-Hadamard type inequalities for s-convex stochastic processes in first sense”, Pure and Applied Mathematics Letters, vol. 2015, pp. 1–7, 2015.
  • N. Mehreen and M. Anwar, “Hermite-Hadamard type inequalities for exponentially p-convex functions and exponentially s-convex functions in the second sense with applications”, Journal of Inequalities and Applications, vol. 2019, no. 92, pp. 1–17, 2019.
  • K. Nikodem, “On convex stochastic processes”, Aequationes Mathematicae, vol. 20, pp. 184–197, 1980.
  • N. Okur, İ. İşcan and E. Yuksek Dizdar, “Hermite-Hadamard type inequalities for p-convex stochastic processes”, An Int. J. Optim. and Cont., vol. 9, no. 2, pp. 148– 153, 2019.
  • M. Z. Sarıkaya, H. Yaldız and H. Budak, “Some integral inequalities for convex stochastic processes”, Acta Math. Univ. Comenianae, LXXXV, pp. 155–164, 2016.
  • E. Set, M. Tomar and S. Maden, “Hermite-Hadamard type inequalities for s-convex stochastic processes in the second sense”, Turkish Journal of Analysis and Number Theory, vol. 2, no. 6, pp. 202–207, 2016.
  • E. Set, M. Z. Sarıkaya and M. Tomar, “Hermite-Hadamard type inequalities for coordinates convex stochastic processes”, Mathematica Aeterna, vol. 5, no. 2, pp. 363–382, 2015.
  • M. Shaked and J. G. Shanthikumar, “Stochastic convexity and its applications”, Advances in Applied Probability, vol. 20, pp. 427–446, 1988.
  • A. Skowronski, “On some properties of J-convex stochastic processes”, Aequationes Mathematicae, vol. 44, pp. 249–258, 1992.
  • M. Tomar, E. Set and S. Maden, “Hermite-Hadamard type inequalities for log-convex stochastic processes”, Journal of New Theory, vol. 2, pp. 23–32, 2015.
  • M. Tomar, E. Set and N. O. Bekar, “Hermite-Hadamard type inequalities for strongly log-convex stochastic processes”, Journal of Global Engineering Studies, vol. 1, no. 53–61, 2014.
Toplam 16 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Araştırma Makalesi
Yazarlar

Serap Özcan 0000-0001-6496-5088

Yayımlanma Tarihi 1 Ekim 2019
Gönderilme Tarihi 6 Mayıs 2019
Kabul Tarihi 24 Haziran 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 23 Sayı: 5

Kaynak Göster

APA Özcan, S. (2019). Hermite-Hadamard Type Inequalities for Exponentially p-Convex Stochastic Processes. Sakarya University Journal of Science, 23(5), 1012-1018. https://doi.org/10.16984/saufenbilder.561040
AMA Özcan S. Hermite-Hadamard Type Inequalities for Exponentially p-Convex Stochastic Processes. SAUJS. Ekim 2019;23(5):1012-1018. doi:10.16984/saufenbilder.561040
Chicago Özcan, Serap. “Hermite-Hadamard Type Inequalities for Exponentially P-Convex Stochastic Processes”. Sakarya University Journal of Science 23, sy. 5 (Ekim 2019): 1012-18. https://doi.org/10.16984/saufenbilder.561040.
EndNote Özcan S (01 Ekim 2019) Hermite-Hadamard Type Inequalities for Exponentially p-Convex Stochastic Processes. Sakarya University Journal of Science 23 5 1012–1018.
IEEE S. Özcan, “Hermite-Hadamard Type Inequalities for Exponentially p-Convex Stochastic Processes”, SAUJS, c. 23, sy. 5, ss. 1012–1018, 2019, doi: 10.16984/saufenbilder.561040.
ISNAD Özcan, Serap. “Hermite-Hadamard Type Inequalities for Exponentially P-Convex Stochastic Processes”. Sakarya University Journal of Science 23/5 (Ekim 2019), 1012-1018. https://doi.org/10.16984/saufenbilder.561040.
JAMA Özcan S. Hermite-Hadamard Type Inequalities for Exponentially p-Convex Stochastic Processes. SAUJS. 2019;23:1012–1018.
MLA Özcan, Serap. “Hermite-Hadamard Type Inequalities for Exponentially P-Convex Stochastic Processes”. Sakarya University Journal of Science, c. 23, sy. 5, 2019, ss. 1012-8, doi:10.16984/saufenbilder.561040.
Vancouver Özcan S. Hermite-Hadamard Type Inequalities for Exponentially p-Convex Stochastic Processes. SAUJS. 2019;23(5):1012-8.

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 Kapak Resmi İndir

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