Several integral inequalities and their applications on means

Document Type : Research Paper


Department of Mathematics, Kharazmi University, Tehran, Iran.


In this paper we prove several sharp inequalities that are new versions and  extensions of Jensen and $H-H$ inequalities. Then we apply them on means.


[1] G. D. Anderson, M. K. Vamanamurtby and M. Vuorinen, Generalized convexity and inequalities, J. Math. Anal. Appl. 335 (2007) 1294–1308.
[2] F. Bruk, The geometric, logarithmic and arithmetic mean inequality, Amer. Math. Month. 94(6) (1987) 527–528.
[3] Y. M. Chu, S. W. Hou and W. F. Xia, Optimal convex combinations bounds of centroidal and harmonic means for logaritmic and identric means, Bull. Iran. Math Soc. 39(2)(2013) 259–269.
[4] O. Kouba, New bounds for the identric mean of two arguments, J. Ineqal. Pure Appl. Math. 9(3) (2008) Article 71, pp.6.
[5] F. Qi and B. N. Guo, An inequality between ratio of the extended logaritmic means and ratio of the exponential means, Taiwanese J. Math, 7(2) (2003) 229–237.
[6] J. Sandor, On certain inequalities for means III, Arch. Math. (Basel) 76(1) (2001) 34–40.
[7] J. Sandor, On the identric and logaritmic means, Aeq. Math. 40(2–3) (1990) 261–270.
[8] J. Sandor, On refinements of certain inequalities for means, Arch. Math .(Brno) 31(4) (1995) 274–282.
[9] M. Z. Sarikaya and H. Budak, On generalized Hermite-Hadamard inequality for generalized convex function, Int. J. Nonlinear Anal. Appl. 8 (2017) 209–222.
[10] M. K. Wang, Z. K. Wang and Y. M. Chu, An optimal double inequality between geometric and identric mean, Appl. Math. Lett. 25(3) (2012) 471–475.
[11] ZH-H. Yang, New sharp bounds for logaritmic mean and identric mean, J. Inequal. Appl. (2013) Article 116.
[12] G. Zabandan, An extension and refinement of Hermite-Hadamard inequalities and related results, Int. J. Nonlinear Anal. Appl. 11(2) (2020) 379–390.
[13] G. Zabandan, Jensen’s inequality for GG-convex functions, Int. J. Nonlinear Anal. Appl. 10(1) (2019) 1–7.
[14] G. Zabandan, Jensen’s inequality for HH-convex functions and related results, Adv. inequal, Appl. (2016) Article 10.
[15] T. Zhang, W. F. Xia, Y. M. Chu and G. D. Wang, Optimal bounds for logaritmic and identric means in terms of generalized centeroidal mean, J. Appl. Anal. 19 (2013) 141–152.
Volume 12, Issue 2
November 2021
Pages 363-374
  • Receive Date: 16 February 2021
  • Accept Date: 20 April 2021