74
Views
2
CrossRef citations to date
0
Altmetric
Research Articles

On Some Inequalities of Differentiable Uniformly Convex Mapping with Applications

& ORCID Icon
Pages 368-381 | Received 28 Jun 2022, Accepted 26 Jan 2023, Published online: 06 Feb 2023

References

  • Bai, R.-F., Qi, F., Xi, B.-Y. (2013). Hermite–Hadamard type inequalities for the m− and (α,m) logarithmically convex functions. Filomat. 27(1):1–7. DOI: 10.1186/s13660-020-02442-5.
  • Bai, S.-P., Qi, F. (2013). Some inequalities for (s1,m1)−(s2,m2)-convex functions on the co-ordinates. Glob. J. Math. Anal. 1(1):22–28. DOI: 10.13140/2.1.2919.7126.
  • Barsam, H., Ramezani, S. M., Sayyari, Y. (2021). On the new Hermite-Hadamard type inequalities for s-convex functions. Afr. Mat. 32(7–8):1355–1367. DOI: 10.1007/s13370-021-00904-7.
  • Barsam, H., Sattarzadeh, A. R. (2020). Hermite-Hadamard inequalities for uniformly convex functions and its applications in means. Miskolc Math. Notes. 21(2):621–630. DOI: 10.18514/MMN.2020.2993.
  • Dragomir, S. S., Pearce, C. E. M. (2000). Selected topics on hermite-hadamard inequalities and applications, RGMIA monographs. Footscray: Victoria University. http://www.staff.vu.edu.au/RGMIA/monographs/hermite hadamard.html
  • Mitrinovic, D. S., Lackovic, I. B. (1985). Hermite and convexity. Aequationes Math. 28(1):229–232. DOI: 10.1007/BF02189414.
  • Gürbüz, M., Özdemir, M. E. (2020). On some inequalities for product of different kinds of convex functions. Turk. J. Sci. 5(1):23–27.
  • Akdemir, A. O., Butt, S. I., Nadeem, M., Ragusa, M. A. (2021). New general variants of Chebyshev type inequalities via generalized fractional integral operators. Mathematics. 9(2):122. DOI: 10.3390/math9020122.
  • Butt, S. I., Nadeem, M., Farid, G. (2020). On Caputo fractional derivatives via exponential s-convex functions. Turk. J. Sci. 5(2):140–146.
  • Sayyari, Y., Barsam, H., Sattarzadeh, A. R. (2023). On new refinement of the Jensen inequality using uniformly convex functions with applications. Appl Anal. 102(1):1–9. DOI: 10.1080/00036811.2023.2171873.
  • Iscan, I. (2014). Hermite–Hadamard–Fejer type inequalities for convex functions via fractional integrals. arXiv14047722v1. 60(3). DOI: 10.48550/arXiv.1404.7722.
  • Minculete, N., Mitroi, F. C. (2012). Fejer–type inequalities. Aust. J. Math. Anal. Appl. 9(1):8pp. DOI: 10.11121/ijocta.01.2017.00405.
  • Sarikaya, M. Z. (2012). On new Hermite-Hadamard Fejer type integral inequalities. Stud. Univ. Babe s Bolyai Math. 57(3):377–386.
  • Fejér, L. (1906). Uber die fourierreihen II. Math. Naturwiss. Anz Ungar. Akad. Wiss. 24:369–390.
  • Sayyari, Y. (2021). An improvement of the upper bound on the entropy of information sources. J. Math. Ext. 15(5):1–12. DOI: 10.30495/JME.SI.2021.1976.
  • Sayyari, Y. (2020). New bounds for entropy of information sources. Wavelets linear Algebr. 7(2):1–9. DOI: 10.22072/WALA.2020.111881.1240.
  • Sayyari, Y. (2020). New entropy bounds via uniformly convex functions. Chaos Sol. Fractals. 141(1):110360. DOI: 10.1016/j.chaos.2020.110360.
  • Sayyari, Y. (2021). New refinements of Shannon’s entropy upper bounds. J. Inf. Optim. Sci. 42(8):1869–1883. DOI: 10.1080/02522667.2021.1966947.
  • Alomari, M., Darus, M., Dragomir, S. S. (2009). New inequalities of Hermite–Hadamard type for functions whose second derivates absolute values are quasi-convex. RGMIA Res. Rep. Coll. 12:14. http://www.staff.vu.edu.au/RGMIA/v12(E).asp.
  • Shuang, Y., Yin, H.-P., Qi, F. (2013). Hermite–Hadamard type integral inequalities for geometric-arithmetically s-convex functions. Analysis (Munich) 33(2):197–208. DOI: 10.22436/jnsa.015.04.01.
  • Hua, J., Xi, B.-Y., Qi, F. (2014). Inequalities of Hermite–Hadamard type involving an s-convex function with applications. Appl. Math. Comput. 246:752–760. DOI: 10.3390/math6110223.
  • Hussain, S., Bhatti, M. I., Iqbal, M. (2009). Hadamard-type inequalities for s-convex functions. Punjab Univ. J. Math. 41:51–60.
  • Hwang, D. Y. (2011). Some inequalities for differentiable convex mapping with application to weighted trapezoidal formula and higher moments of random variables. Appl. Math. Comput. 217(23):9598–9605. DOI: 10.1016/j.amc.2011.04.036.
  • Ion, D. A. (2007). Some estimates on the Hermite-Hadamard inequality through quasi-convex functions. Ann. Univ. Craiova Math. Comp. Sci. Ser. 34:82–87.
  • Özdemir, M. E., Avcı, M., Set, E. (2010). On some inequalities of Hermite–Hadamard type via m-convexity. Appl. Math. Lett. 23(9):1065–1070. DOI: 10.1016/j.aml.2010.04.037.
  • Xi, B.-Y., Qi, F. (2013). Some Hermite–Hadamard type inequalities for differentiable convex functions and applications. Hacet. J. Math. Stat. 42(3):243– 257.
  • Mehrez, K., Agarwal, P. (2019). New Hermite–Hadamard type integral inequalities for convex functions and their applications. J. Comput. Appl. Math. 350:274–285. DOI: 10.1016/j.cam.2018.10.022.
  • Mohammed, P. O., Abdeljawad, T., Baleanu, D., Kashuri, A., Hamasalh, F., Agarwal, P. (2020). New fractional inequalities of Hermite-Hadamard type involving the incomplete gamma functions. J. Inequal. Appl. 2020(1):1–16. DOI: 10.1186/s13660-020-02538-y.
  • Jain, S., Mehrez, K., Baleanu, D., Agarwal, P. (2019). Certain Hermite–Hadamard inequalities for logarithmically convex functions with applications. Mathematics 7(2):163. DOI: 10.3390/math7020163.
  • Agarwal, P., Jleli, M., Tomar, M. (2017). Certain Hermite–Hadamard type inequalities via generalized k-fractional integrals. J. Inequal. Appl. 2017(1):55. DOI: 10.1186/s13660-017-1318-y.
  • Cortez, M. V., Ali, M. A., Budak, H., Kalsoom, H., Agarwal, P. (2021). Some new Hermite–Hadamard and related inequalities for convex functions via (p,q)-integral. Entropy 23(7):828. DOI: 10.3390/e23070828.
  • Xi, B.-Y., Qi, F. (2013). Some inequalities of Hermite–Hadamard type for h-convex functions. Adv. Inequal. Appl. 2(1):1–15.
  • Özdemir, M. E., Set, E., Akdemir, A. O., Sarikaya, M. Z. (2015). Some new Chebyshev type inequalities for functions whose derivatives belongs to spaces. Afr. Mat. 26(7–8):1609–1619. DOI: 10.1007/s13370-014-0312-5.
  • Zhang, T.-Y., Ji, A.-P., Qi, F. (2013). Integral inequalities of Hermite–Hadamard type for harmonically quasi-convex functions. Proc. Jangjeon Math. Soc. 16(3):399–407.
  • Xi, B.-Y., Qi, F. (2013). Hermite–Hadamard type inequalities for functions whose derivatives are of convexities. Nonlinear Funct. Anal. Appl. 18(2):163– 176.
  • Dragomir, S. S., Agarwal, R. P. (1998). Two inequalities for differentiable mappings and applications to special means of real numbers and to Trapezoidal formula. Appl. Math. Lett. 11(5):91–95. DOI: 10.1080/02522667.2021.1966947.
  • Bauschke, H. H., Combettes, P. L. (2011). Convex analysis and Monotone Operator Theory in Hilbert Spaces. New York, NY: Springer-Verlag.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.