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Year 2020, Volume: 41 Issue: 4, 845 - 853, 29.12.2020

Nurgül Okur

https://doi.org/10.17776/csj.634250

Abstract

References

  • [1] Hadamard J., Étude sur les propriétés des fonctions entières et en particulier d.une function considerée par Riemann, J. Math Pures Appl., 58 (1893) 171-215.
  • [2] Alomari M.W., A generalization of Hermite-Hadamard’s inequality, Krag. J. Math., 41(2) (2017) 313–328.
  • [3] Dragomir S.S., On Hadamard’s inequality for convex functions on the coordinates in a rectangle from the plane, Taiwanese J. Math., 4 (2001) 775–788.
  • [4] Nwaeze E.R., Generalized Hermite-Hadamard’s inequality for functions convex on the coordinates, Applied Mathematics E-Notes, 18 (2018) 275-283.
  • [5] Hanson M.A., On sufficiency of the Kuhn-Tucker conditions. Journal of Mathematical Analysis and Applications, 80 (1981) 545-550.
  • [6] Ben-Isreal A., Mond B., What is invexity? Journal of Australian Mathematical Society, Series B., 28(1) (1986) 1-9.
  • [7] Noor M.A., Hermite-Hadamard integral inequalities for log-preinvex functions, Journal of Mathematical Analysis and Approximation Theory, 2 (2007) 126-131.
  • [8] Mohan S.R., Neogy S.K., On invex sets and preinvex functions, Journal of Mathematical Analysis and Applications, 189 (1995) 901-908.
  • [9] Pini R., Invexity and generalized Convexity. Optimization, 22 (1991) 513-525.
  • [10] Weir T., Mond B., Preinvex functions in multiple bijective optimization, Journal of Mathematical Analysis and Applications, 136 (1998) 29-38.
  • [11] Yang X.M., Li D., On properties of preinvex functions, J. Math. Anal. Appl, 256 (2001) 229-241.
  • [12] Noor, M.A., Invex equilibrium problems, J. Math. Anal. Appl., 302 (2005) 463-475.
  • [13] Mishra S.K., Giorgi G., Invexity and optimization, Nonconvex optimization and Its Applications, Vol.88, Berlin: Springer-Verlag, 2008.
  • [14] Kumar P., Inequalities involving moments of a continuous random variable defined over a finite interval, Computers and Math. with Appl., 48 (2004) 257-273.
  • [15] Gavrea B.A, Hermite–Hadamard type inequality with applications to the estimation of moments of continuous random variables, Appl. Math. and Comp, 254 (2015) 92-98.
  • [16] Feller W., An introduction to Probability Theory and its Applications, Vol.2, New York: J John Wiley, 1971.
  • [17] Ross S.M., Stochastic Processes, 2rd ed.; J.Wiley&Sons, 1996.
  • [18] Nikodem K., On convex stochastic processes, Aequat. Math., 20 (1980) 184-197.
  • [19] Kotrys D., Hermite-Hadamard inequality for convex stochastic processes, Aequat. Math., 83 (2012) 143-151.
  • [20] Okur N., Multidimensional general convexity for stochastic processes and associated witH Hermite-Hadamard type integral inequalities, Thermal Sci., Suppl. 6(23) (2019), 1971-1979.
  • [21] Okur N., Aliyev R., Some Hermite-Hadamard type integral inequalities for multidimensional general preinvex stochastic processes, Comm. Statist. Theory Methods, 49 (2020), in press.
  • [22] Set E., Sarıkaya M.Z., Tomar M., Hermite-Hadamard inequalities for coordinates convex stochastic processes, Mathematica Aeterna, 5 (2) (2015) 363-382.
  • [23] Akdemir G.H., Okur B. N., Iscan,I., On Preinvexity for Stochastic Processes, Statistics, Journal of the Turkish Statistical Association, 7(1) (2014) 15-22.
  • [24] Okur B. N., Gunay Akdemir H., Iscan I., Some extensions of preinvexity for stochastic processes, Comp. Analysis, Springer Proceedings in Mathematics & Statistics,, New York: Springer, 2016; 155, 259-270.
  • [25] Usta Y., Stokastik Süreçler için Koordinatlarda Bazı Konvekslik Çeşitleri ve Hermite-Hadamard Eşitsizliği, Yüksek Lisans Tezi, Giresun Üniversitesi, Fen Bilimleri Enstitüsü, 2018.

Some generalised integral inequalities for bidimensional preinvex stochastic processes

Year 2020, Volume: 41 Issue: 4, 845 - 853, 29.12.2020

Nurgül Okur

https://doi.org/10.17776/csj.634250

Abstract

In this study, we generalized some integral inequalities
for bidimensional preinvex stochastic processes. For this reason, we used
mean-square integrable preinvex stochastic processes on the real line and on the
coordinates, respectively. Therefore, we obtained some generalized integral
inequalitİies for preinvex stochastic processes on the real line.

Keywords

Hermite-Hadamard tipli integral eşitsizliği (HHII) kuadratik orta anlamda integral iki boyutlu preinveks stokastik süreçler (P_η^2SP)

References

  • [1] Hadamard J., Étude sur les propriétés des fonctions entières et en particulier d.une function considerée par Riemann, J. Math Pures Appl., 58 (1893) 171-215.
  • [2] Alomari M.W., A generalization of Hermite-Hadamard’s inequality, Krag. J. Math., 41(2) (2017) 313–328.
  • [3] Dragomir S.S., On Hadamard’s inequality for convex functions on the coordinates in a rectangle from the plane, Taiwanese J. Math., 4 (2001) 775–788.
  • [4] Nwaeze E.R., Generalized Hermite-Hadamard’s inequality for functions convex on the coordinates, Applied Mathematics E-Notes, 18 (2018) 275-283.
  • [5] Hanson M.A., On sufficiency of the Kuhn-Tucker conditions. Journal of Mathematical Analysis and Applications, 80 (1981) 545-550.
  • [6] Ben-Isreal A., Mond B., What is invexity? Journal of Australian Mathematical Society, Series B., 28(1) (1986) 1-9.
  • [7] Noor M.A., Hermite-Hadamard integral inequalities for log-preinvex functions, Journal of Mathematical Analysis and Approximation Theory, 2 (2007) 126-131.
  • [8] Mohan S.R., Neogy S.K., On invex sets and preinvex functions, Journal of Mathematical Analysis and Applications, 189 (1995) 901-908.
  • [9] Pini R., Invexity and generalized Convexity. Optimization, 22 (1991) 513-525.
  • [10] Weir T., Mond B., Preinvex functions in multiple bijective optimization, Journal of Mathematical Analysis and Applications, 136 (1998) 29-38.
  • [11] Yang X.M., Li D., On properties of preinvex functions, J. Math. Anal. Appl, 256 (2001) 229-241.
  • [12] Noor, M.A., Invex equilibrium problems, J. Math. Anal. Appl., 302 (2005) 463-475.
  • [13] Mishra S.K., Giorgi G., Invexity and optimization, Nonconvex optimization and Its Applications, Vol.88, Berlin: Springer-Verlag, 2008.
  • [14] Kumar P., Inequalities involving moments of a continuous random variable defined over a finite interval, Computers and Math. with Appl., 48 (2004) 257-273.
  • [15] Gavrea B.A, Hermite–Hadamard type inequality with applications to the estimation of moments of continuous random variables, Appl. Math. and Comp, 254 (2015) 92-98.
  • [16] Feller W., An introduction to Probability Theory and its Applications, Vol.2, New York: J John Wiley, 1971.
  • [17] Ross S.M., Stochastic Processes, 2rd ed.; J.Wiley&Sons, 1996.
  • [18] Nikodem K., On convex stochastic processes, Aequat. Math., 20 (1980) 184-197.
  • [19] Kotrys D., Hermite-Hadamard inequality for convex stochastic processes, Aequat. Math., 83 (2012) 143-151.
  • [20] Okur N., Multidimensional general convexity for stochastic processes and associated witH Hermite-Hadamard type integral inequalities, Thermal Sci., Suppl. 6(23) (2019), 1971-1979.
  • [21] Okur N., Aliyev R., Some Hermite-Hadamard type integral inequalities for multidimensional general preinvex stochastic processes, Comm. Statist. Theory Methods, 49 (2020), in press.
  • [22] Set E., Sarıkaya M.Z., Tomar M., Hermite-Hadamard inequalities for coordinates convex stochastic processes, Mathematica Aeterna, 5 (2) (2015) 363-382.
  • [23] Akdemir G.H., Okur B. N., Iscan,I., On Preinvexity for Stochastic Processes, Statistics, Journal of the Turkish Statistical Association, 7(1) (2014) 15-22.
  • [24] Okur B. N., Gunay Akdemir H., Iscan I., Some extensions of preinvexity for stochastic processes, Comp. Analysis, Springer Proceedings in Mathematics & Statistics,, New York: Springer, 2016; 155, 259-270.
  • [25] Usta Y., Stokastik Süreçler için Koordinatlarda Bazı Konvekslik Çeşitleri ve Hermite-Hadamard Eşitsizliği, Yüksek Lisans Tezi, Giresun Üniversitesi, Fen Bilimleri Enstitüsü, 2018.
There are 25 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Natural Sciences
Authors

Nurgül Okur 0000-0002-2544-7752

Publication Date December 29, 2020
Submission Date October 17, 2019
Acceptance Date November 20, 2020
Published in Issue Year 2020Volume: 41 Issue: 4

Cite

APA Okur, N. (2020). Some generalised integral inequalities for bidimensional preinvex stochastic processes. Cumhuriyet Science Journal, 41(4), 845-853. https://doi.org/10.17776/csj.634250