Inequalities of Hermite–Hadamard type for GA-convex functions

Sever S. Dragomir

Published: 2018-05-14

Vol. 32 (2018)

Inequalities of Hermite–Hadamard type for GA-convex functions

Sever S. Dragomir

Abstract

Some inequalities of Hermite–Hadamard type for GA-convex functions defined on positive intervals are given.

Keywords:

Hermite–Hadamard type inequalities , convex functions , integral inequalities , GA-convex functions

Download files

PDF

Citation rules

Dragomir, S. S. (2018). Inequalities of Hermite–Hadamard type for GA-convex functions. Annales Mathematicae Silesianae, 32, 145–168. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/13918

Similar Articles

Silvestru Sever Dragomir, Gradient inequalities for an integral transform of positive operators in Hilbert spaces , Annales Mathematicae Silesianae: Vol. 37 No. 2 (2023)
McSylvester Ejighikeme Omaba, Eze R. Nwaeze, Generalized fractional inequalities of the Hermite-Hadamard type for convex stochastic processes , Annales Mathematicae Silesianae: Vol. 35 No. 1 (2021)
Sever S. Dragomir, Reverse Jensen’s type trace inequalities for convex functions of selfadjoint operators in Hilbert spaces , Annales Mathematicae Silesianae: Vol. 30 (2016)
Antonio Azócar, Kazimierz Nikodem, Gari Roa, Fejér-type inequalities for strongly convex functions , Annales Mathematicae Silesianae: Vol. 26 (2012)
Kazimierz Nikodem, Teresa Rajba, Ohlin and Levin-Stečkin-type results for strongly convex functions , Annales Mathematicae Silesianae: Vol. 34 No. 1 (2020)
Mea Bombardelli, Sanja Varošanec, Strongly M_φM_ψ-convex functions, the Hermite-Hadamard-Fejér inequality and related results , Annales Mathematicae Silesianae: Vol. 38 No. 2 (2024)
Ghulam Farid, Atiq ur Rehman, Generalizations of some integral inequalities for fractional integrals , Annales Mathematicae Silesianae: Vol. 32 (2018)
Mochamed Akkouchi, Mochamed Amine Ighachane, Refinements of some recent inequalities for certain special functions , Annales Mathematicae Silesianae: Vol. 33 (2019)
Badreddine Meftah, Some new Ostrowski’s inequalities for functions whose nth derivatives are logarithmically convex , Annales Mathematicae Silesianae: Vol. 32 (2018)
Teodoro Lara, Nelson Merentes, Edgar Rosales, Ambrosio Tineo, Properties and characterizations of convex functions on time scales , Annales Mathematicae Silesianae: Vol. 32 (2018)

1 2 3 4 5 6 7 8 9 10 > >>

You may also start an advanced similarity search for this article.

References

1. Anderson G.D., Vamanamurthy M.K., Vuorinen M., Generalized convexity and inequalities, J. Math. Anal. Appl. 335 (2007), no. 2, 1294–1308.
2. Beckenbach E.F., Convex functions, Bull. Amer. Math. Soc. 54 (1948), no. 5, 439–460.
3. Bombardelli M., Varošanec S., Properties of h-convex functions related to the Hermite–Hadamard–Fejér inequalities, Comput. Math. Appl. 58 (2009), no. 9, 1869–1877.
4. Cristescu G., Hadamard type inequalities for convolution of h-convex functions, Ann. Tiberiu Popoviciu Semin. Funct. Equ. Approx. Convexity 8 (2010), 3–11.
5. Dragomir S.S., An inequality improving the first Hermite–Hadamard inequality for convex functions defined on linear spaces and applications for semi-inner products, JIPAM. J. Inequal. Pure Appl. Math. 3 (2002), no. 2, Article 31, 8 pp.
6. Dragomir S.S., An inequality improving the second Hermite–Hadamard inequality for convex functions defined on linear spaces and applications for semi-inner products, JIPAM. J. Inequal. Pure Appl. Math. 3 (2002), no. 3, Article 35, 8 pp.
7. Dragomir S.S., An Ostrowski like inequality for convex functions and applications, Rev. Math. Complut. 16 (2003), no. 2, 373–382.
8. Dragomir S.S., Fitzpatrick S., The Hadamard inequalities for s-convex functions in the second sense, Demonstratio Math. 32 (1999), no. 4, 687–696.
9. Dragomir S.S., Fitzpatrick S., The Jensen inequality for s-Breckner convex functions in linear spaces, Demonstratio Math. 33 (2000), no. 1, 43–49.
10. Dragomir S.S., Mond B., On Hadamard’s inequality for a class of functions of Godunova and Levin, Indian J. Math. 39 (1997), no. 1, 1–9.
11. Dragomir S.S., Pearce C.E.M., On Jensen’s inequality for a class of functions of Godunova and Levin, Period. Math. Hungar. 33 (1996), no. 2, 93–100.
12. Dragomir S.S., Pearce C.E.M., Quasi-convex functions and Hadamard’s inequality, Bull. Austral. Math. Soc. 57 (1998), no. 3, 377–385.
13. Dragomir S.S., Pečarić J., Persson L.E., Some inequalities of Hadamard type, Soochow J. Math. 21 (1995), no. 3, 335–341.
14. Dragomir S.S., Rassias Th.M. (eds.), Ostrowski Type Inequalities and Applications in Numerical Integration, Kluwer Academic Publisher, Dordrecht, 2002.
15. Godunova E.K., Levin V.I., Inequalities for functions of a broad class that contains convex, monotone and some other forms of functions, Numerical mathematics and mathematical physics, 138–142, 166, Moskov. Gos. Ped. Inst., Moscow, 1985 (in Russian).
16. Noor M.A., Noor K.I., Awan M.U., Some inequalities for geometrically-arithmetically h-convex functions, Creat. Math. Inform. 23 (2014), no. 1, 91–98.
17. Zhang X.-M., Chu Y.-M., Zhang X.-H., The Hermite–Hadamard type inequality of GAconvex functions and its application, J. Inequal. Appl. 2010, Art. ID 507560, 11 pp. Google Scholar

Vol. 32 (2018)
Published: 2018-08-24

ISSN: 0860-2107

eISSN: 2391-4238

10.1515/amsil

Publisher

University of Silesia Press

Submit