Inequalities of Hermite–Hadamard Type for GA-Convex Functions

Sever S. Dragomir

doi:10.2478/amsil-2018-0001

.blurhash-client-img { display: none !important; }

Inequalities of Hermite–Hadamard Type for GA-Convex Functions

Annales Mathematicae Silesianae

Volume 32 (2018): Issue 1 (September 2018)

By: Sever S. Dragomir

Open Access

|Aug 2018

Abstract

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

References

[1] Anderson G.D., Vamanamurthy M.K., Vuorinen M., Generalized convexity and inequalities, J. Math. Anal. Appl. 335 (2007), no. 2, 1294-1308.10.1016/j.jmaa.2007.02.016
Search in Google Scholar Back to article
[2] Beckenbach E.F., Convex functions, Bull. Amer. Math. Soc. 54 (1948), no. 5, 439-460.10.1090/S0002-9904-1948-08994-7
Search in Google Scholar Back to article
[3] Bombardelli M., Varošanec S., Properties of h-convex functions related to the Hermite- Hadamard-Fejér inequalities, Comput. Math. Appl. 58 (2009), no. 9, 1869-1877.10.1016/j.camwa.2009.07.073
Open DOI Search in Google Scholar Back to article
[4] Cristescu G., Hadamard type inequalities for convolution of h-convex functions, Ann. Tiberiu Popoviciu Semin. Funct. Equ. Approx. Convexity 8 (2010), 3-11.
Search in Google Scholar Back to article
[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.
Search in Google Scholar Back to article
[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.
Search in Google Scholar Back to article
[7] Dragomir S.S., An Ostrowski like inequality for convex functions and applications, Rev. Math. Complut. 16 (2003), no. 2, 373-382.10.5209/rev_REMA.2003.v16.n2.16807
Search in Google Scholar Back to article
[8] Dragomir S.S., Fitzpatrick S., The Hadamard inequalities for s-convex functions in the second sense, Demonstratio Math. 32 (1999), no. 4, 687-696.10.1515/dema-1999-0403
Search in Google Scholar Back to article
[9] Dragomir S.S., Fitzpatrick S., The Jensen inequality for s-Breckner convex functions in linear spaces, Demonstratio Math. 33 (2000), no. 1, 43-49.10.1515/dema-2000-0106
Search in Google Scholar Back to article
[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.
Search in Google Scholar Back to article
[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, 93-100.10.1007/BF02093506
Search in Google Scholar Back to article
[12] Dragomir S.S., Pearce C.E.M., Quasi-convex functions and Hadamard’s inequality, Bull. Austral. Math. Soc. 57 (1998), no. 3, 377-385.10.1017/S0004972700031786
Open DOI Search in Google Scholar Back to article
[13] Dragomir S.S., Pecaric J., Persson L.E., Some inequalities of Hadamard type, Soochow J. Math. 21 (1995), no. 3, 335-341.
Search in Google Scholar Back to article
[14] Dragomir S.S., Rassias Th.M. (eds.), Ostrowski Type Inequalities and Applications in Numerical Integration, Kluwer Academic Publisher, Dordrecht, 2002.10.1007/978-94-017-2519-4
Search in Google Scholar Back to article
[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).
Search in Google Scholar Back to article
[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, 91-98.10.37193/CMI.2014.01.14
Search in Google Scholar Back to article
[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.10.1155/2010/507560
Search in Google Scholar Back to article

Articles in this issue

DOI: https://doi.org/10.2478/amsil-2018-0001 | Journal eISSN: 2391-4238 | Journal ISSN: 0860-2107

Journal RSS Feed

Language: English

Page range: 145 - 168

Submitted on: Apr 11, 2017

Accepted on: Jan 27, 2018

Published on: Aug 24, 2018

Published by: University of Silesia in Katowice, Institute of Mathematics

In partnership with: Paradigm Publishing Services

Publication frequency: 2 issues per year

Keywords:

Hermite-Hadamard type inequalities,

convex functions,

integral inequalities,

GA-convex functions

Related subjects:

Mathematics,

General mathematics

© 2018 Sever S. Dragomir, published by University of Silesia in Katowice, Institute of Mathematics
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 32 (2018): Issue 1 (September 2018)