Some new inequalities of Hermite-Hadamard type for GA-convex functions

Sever S. Dragomir

Abstract


Some new inequalities of Hermite-Hadamard type for GA-convex functions defined on positive intervals are given. Refinements and weighted version of known inequalities are provided. Some applications for special means are also obtained.

Keywords


Convex functions; integral inequalities; GA-convex functions; Hermite-Hadamard inequalities

Full Text:

PDF

References


Alomari, M., Darus, M., The Hadamard’s inequality for s-convex function, Int. J. Math. Anal. (Ruse) 2 (2008), no. 13-16, 639-646.

Anderson, G. D., Vamanamurthy, M. K., Vuorinen, M., Generalized convexity and inequalities, J. Math. Anal. Appl. 335 (2007) 1294-1308.

Beckenbach, E. F., Convex functions, Bull. Amer. Math. Soc. 54 (1948), 439-460.

Cristescu, G., Hadamard type inequalities for convolution of h-convex functions, Ann. Tiberiu Popoviciu Semin. Funct. Equ. Approx. Convexity 8 (2010), 3-11.

Dragomir, S. S., Some remarks on Hadamard’s inequalities for convex functions, Extracta Math. 9 (2) (1994), 88-94.

Dragomir, S. S., An inequality improving the first Hermite–Hadamard inequality for convex functions defined on linear spaces and applications for semi-inner products. J. Inequal. Pure Appl. Math. 3 (2) (2002), Article 31, 8 pp.

Dragomir, S. S., An inequality improving the second Hermite–Hadamard inequality for convex functions defined on linear spaces and applications for semi-inner products, J. Inequal. Pure Appl. Math. 3 (3) (2002), Article 35, 18 pp.

Dragomir, S. S., An Ostrowski like inequality for convex functions and applications, Revista Math. Complutense 16 (2) (2003), 373-382.

Dragomir, S. S., Operator Inequalities of Ostrowski and Trapezoidal Type, Springer, New York, 2012.

Dragomir, S. S., Inequalities of Hermite–Hadamard type for GA-convex functions, Preprint RGMIA Res. Rep. Coll.

Dragomir, S. S., Cerone, P., Roumeliotis J., Wang, S., A weighted version of Ostrowski inequality for mappings of Holder type and applications in numerical analysis, Bull. Math. Soc. Sci. Math. Romanie 42 (90) (4) (1999), 301-314.

Dragomir, S. S., Fitzpatrick, S., The Hadamard inequalities for s-convex functions in the second sense, Demonstratio Math. 32 (4) (1999), 687-696.

Dragomir, S. S., Fitzpatrick, S., The Jensen inequality for s-Breckner convex functions in linear spaces, Demonstratio Math. 33 (1) (2000), 43-49.

Dragomir, S. S., Mond, B., On Hadamard’s inequality for a class of functions of Godunova and Levin, Indian J. Math. 39 (1) (1997), 1-9.

Dragomir, S. S., Pearce, C. E. M., On Jensen’s inequality for a class of functions of Godunova and Levin, Period. Math. Hungar. 33 (2) (1996), 93-100.

Dragomir, S. S., Pearce, C. E. M., Quasi-convex functions and Hadamard’s inequality, Bull. Austral. Math. Soc. 57 (1998), 377-385.

Dragomir, S. S., Pearce, C. E. M., Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA Monographs, Victoria University, 2000 [Online http://rgmia.org/monographs/hermite hadamard.html].

Dragomir, S. S., Pecaric, J., Persson, L., Some inequalities of Hadamard type, Soochow J. Math. 21 (3) (1995), 335-341.

Dragomir, S. S., Rassias, Th. M., (Eds), Ostrowski Type Inequalities and Applications in Numerical Integration, Kluwer Academic Publisher, 2002.

El Farissi, A., Simple proof and refinement of Hermite–Hadamard inequality, J. Math.Ineq. 4 (3) (2010), 365-369.

Kirmaci, U. S., Klaricic Bakula, M., Ozdemir, M. E., Pecaric, J., Hadamard-type inequalities for s-convex functions, Appl. Math. Comput. 193 (1) (2007), 26-35.

Latif, M. A., On some inequalities for h-convex functions, Int. J. Math. Anal. (Ruse) 4 (29–32) (2010), 1473-1482.

Mitrinovic, D. S., Lackovic, I. B., Hermite and convexity, Aequationes Math. 28 (1985), 229-232.

Mitrinovic, D. S., Pecaric, J. E., Note on a class of functions of Godunova and Levin, C. R. Math. Rep. Acad. Sci. Canada 12 (1) (1990), 33-36.

Noor, M. A., Noor, K. I., Awan, M. U., Some inequalities for geometrically-arithmetically h-convex functions, Creat. Math. Inform. 23 (1) (2014), 91-98.

Pearce, C. E. M., Rubinov, A. M., P-functions, quasi-convex functions, and

Hadamard-type inequalities, J. Math. Anal. Appl. 240 (1) (1999), 92-104.

Pecaric, J. E., Dragomir, S. S., On an inequality of Godunova-Levin and some refinements of Jensen integral inequality, Itinerant Seminar on Functional Equations, Approximation and Convexity (Cluj-Napoca, 1989), 263-268, Preprint, 89-6, Univ. “Babe's-Bolyai”, Cluj-Napoca, 1989.

Zhang, X.-M., Chu, Y.-M., Zhang, X.-H., The Hermite–Hadamard type inequality of GA-convex functions and its application, J. Inequal. Appl. vol. 2010, Article 507560, 11 pp.




DOI: http://dx.doi.org/10.17951/a.2018.72.1.55-68
Date of publication: 2018-06-25 09:04:05
Date of submission: 2018-06-24 22:28:30


Statistics


Total abstract view - 1324
Downloads (from 2020-06-17) - PDF - 1073

Indicators



Refbacks

  • There are currently no refbacks.


Copyright (c) 2018 Sever S. Dragomir