# Some Fejer Type Inequalities for Harmonically-Convex Functions with Applications to Special Means

## Main Article Content

### Abstract

In this paper, the notion of harmonic symmetricity of functions is introduced. A new identity involving harmonically symmetric functions is established and some new Fejer type integral inequalities are presented for the class of harmonically convex functions. The results presented in this paper are better than those established in recent literature concerning harmonically convex functions. Applications of our results to special means of positive real numbers are given as well.

## Article Details

### References

- P. S. Bullen, Handbook of Means and Their Inequalities, Mathematics and its Applications, Volume 560, Kluwer Academic Publishers, Dordrecht/Boston/London, 2003.
- F. Chen and S. Wu, Hermite-Hadamard type inequalities for harmonically s-convex functions, Sci. World J. 2014 (2014), Article ID 279158.
- S. S. Dragomir, R.P. Agarwal, Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula, Appl. Math. Lett. 11 (5) (1998), 91-95.
- S. S. Dragomir, C.E.M. Pearce, Selected topics on Hermite-Hadamard type inequalities and applications, RGMIA Monographs, Victoria University, 2000.
- V. N. Huy and N. T. Chung, Some generalizations of the Fej ´ er and Hermite-Hadamard inequalities in HÃ¶lder spaces, J. Appl. Math. Inform. 29 (3-4) (2011), 859-868.
- J. Hua, B.-Y. Xi, and F. Qi, Hemite-Hadamard type inequalities for geometrically-arithmetically s-convex functions, Commun. Korean Math. Soc. 29 (1) (2014), 51-63.
- J. Hua, B. -Y. Xi and F. Qi, Inequalities of Hermite-Hadamard type involving an s-convex function with applications, Applied Mathematics and Computation, 246 (2014), 752-760.
- I. Iscan, Hemite-Hadamard type inequalities for GA-s-convex functions, Le Matematiche, 69 (2) (2014), 129-146.
- I. Iscan, Hermite-Hadamard type inequalities for harmonically convex functions, Hacettepe Journal of Mathematics and Statistics 43 (6) (2014), 935-942.
- I. Iscan, Hermite-Hadamard and Simpson-like type inequalities for differentiable harmonically convex functions, Journal of Mathematics, 2014 (2014), Article ID 346305.
- I. Iscan and S. Wu, Hermite-Hadamard type inequalities for harmonically convex functions via fractional integrals, Applied Mathematica and Computation, 238 (2014), 237-244.
- A. P. Ji, T. Y. Zhang, F. Qi, Integral Inequalities of Hermite-Hadamard Type for (α,m)-GA-Convex Functions, Journal of Function Spaces and Applications, 2013 (2013), Article ID 823856.
- M. A. Latif, New Hermite-Hadamard type integral inequalities for GA-convex functions with applications, Analysis 34 (4) (2014), 379-389.
- M. V. Mihai, M. A. Noor, K. I. Noor and M. U. Awan, Some integral inequalities for harmonic h-convex functions involving hypergeometric functions, Applied Mathematics and Computation 252 (2015), 257-262.
- M. A. Noor, K. I. Noor and M. U. Awana, Integral inequalities for coordinated harmonically convex functions, Complex Var. Elliptic Eqn. 60 (6) (2015), 776-786.
- M. A. Noor, K. I. Noor, M. U. Awana and S. Costache, Some integral inequalities for harmonically h-convex functions, U.P.B Sci. Bull. Serai A. 77 (1) (2015), 5-16.
- M. Z. Sarikaya, On new Hermite Hadamard Fej ´ er type integral inequalities, Stud. Univ. Babe ¸ s-Bolyai Math. 57 (3) (2012), 377-386.
- Y. Shuang, H. P. Yin, F. Qi, Hermite-Hadamard type integral inequalities for geometric-arithmetically s-convex functions, Analysis 33 (2013), 1001-1010.
- B. -Y. Xi and F. Qi, Hemite-Hadamard type inequalities for geometrically r-convex functions, Studia Scientiarum Mathematicarum Hungarica 51 (4) (2014), 530-546.
- T. Y. Zhang, A. P. Ji, F. Qi, Some inequalities of Hermite-Hadamard type for GA-Convex functions with applications to means. Le Matematiche, 48 (1) (2013), 229-239.
- T. -Y. Zhang, A. -P. Ji and F. Qi, Integral inequalities of Hermite-Hadamard type for harmonically quasi-convex functions, Proceedings of the Jangjeon Mathematical Society, 16(3) (2013), 399-407.