Fejer Type Inequalities for Harmonically (s,m)-Convex Functions

Baloch, Imran Abbas; Icscan, Imdat; Dragomir, Silvestru Sever

Research Article

Fejer Type Inequalities for Harmonically (s,m)-Convex Functions

Imran Abbas Baloch¹*
Imdat Icscan²
Silvestru Sever Dragomir³

Abdus Salam School of Mathematical Sciences, GC University, Lahore, Pakistan.
Department of Mathematics, Faculty of Arts and Sciences, Giresun University, 28200, Giresun, Turkey.
Mathematics, College of Engineering and Science, Victoria University, Melbourne City, Australia.

* Corresponding author

Abstract

In this paper, a new weighted identity involving harmonically symmetric functions and differentiable functions is established. By using the notion of harmonic symmetricity, harmonic (s,m)-convexity, analysis and some auxiliary results, some new Fejér type integral inequalities are presented for the class of harmonically (s,m)-convex functions.

How to Cite

I. A. Baloch, I. Icscan, S. S. Dragomir, Fejer Type Inequalities for Harmonically (s,m)-Convex Functions, Int. J. Anal. Appl. 12 (2016), 188–197.

BibTeX

@article{Baloch2016,
  author  = {Baloch, Imran Abbas and Icscan, Imdat and Dragomir, Silvestru Sever},
  title   = {Fejer Type Inequalities for Harmonically (s,m)-Convex Functions},
  journal = {Int. J. Anal. Appl.},
  volume  = {12},
  year    = {2016},
  pages   = {188--197},
  doi     = {}
}

References

[1] I. A. Baloch, I.IÅŸcan, Some Ostrowski Type Inequalities For Harmonically (s,m)-convex functoins in Second Sense, International Journal of Analysis, 2015 (2015), Article ID 672675.
[2] P. S. Bullen, Handbook of Means and Their Inequalities, Mathematics and its Applications, Volume 560, Kluwer Academic Publishers, Dordrecht/Boston/London, 2003.
[3] W.W. Breckner, tetigkeitsaussagen f ¨ ur eine klasse verallgemeinerter konvexer funktonen in topologischen lin- earen Räumen, Publ. Inst. Math. (Beograd), 23 (1978),13-20.
[4] F. Chen and S. Wu, Fejér and Hermite-Hadamard type inequalities for harmonically convex functions, Journal of Applied Mathematics 2014 (2014), Article ID 386806.
[5] F. Chen and S.Wu, Hermite-Hadamard type inequalities for harmonically s-convex functions, Sci. World J. 2014 (2014), Article ID 279158.
[6] 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.
[7] S. S. Dragomir, C.E.M. Pearce, Selected topics on Hermite-Hadamard type inequalities and applications, RGMIA Monographs, Victoria University, 2000.
[8] V. N. Huy and N. T. Chung, Some generalizations of the Fejér and Hermite-Hadamard inequalities in Hölder spaces, J. Appl. Math. Inform. 29 (2011), no. 3-4, 859-868.
[9] J. Hua, B.-Y. Xi, and F. Qi, Hemite-Hadamard type inequalities for geometrically- arithmetically s-convex functions, Commun. Korean Math. Soc. 29 (2014), No. 1, 51-63.
[10] J. Hua, B. -Y. Xi and F. Qi, Inequalities of HermiteHadamard type involving an s-convex function with applications, Applied Mathematics and Computation, 246 (2014), 752-760.
[11] I.IÅŸcan, Hemite-Hadamard type inequalities for GA-s-convex functions, Le Matematiche, 69 (2014), 129-146.
[12] I.IÅŸcan, Hermite-Hadamard type inequalities for harmonically convex functions, Hacettepe Journal of Mathematics and Statistics 43 (6) (2014), 935-942.
[13] I.IÅŸcan, Ostrowski type inequalities for harmonically s-convex functions, Konuralp Journal of Mathematics, 3 (2015), no. 1, 63-74.
[14] I.IÅŸcan, Hermite-Hadamard and Simpson-like type inequalities for differentiable harmonically convex functions, Journal of Mathematics, 2014 (2014), Article ID 346305.
[15] I.IÅŸcan and S. Wu, Hermite-Hadamard type inequalities for harmonically convex functions via fractional integrals, Applied Mathematica and Computation, 238 (2014), 237-244.
[16] 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.
[17] M. A. Latif, New Hermite-Hadamard type integral inequalities for GA-convex functions with applications, Analysis, 34 (2014), 379-389.
[18] 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 Computa- tion 252 (2015), 257-262.
[19] M. A. Noor, K. I. Noor and M. U. Awana, Integral inequalities for coordinated harmonically convex functions, Complex Var. Elliptic Eqn. 60 (2015), 776-786.
[20] M. A. Noor, K. I. Noor, M. U. Awana and S. Costache, Some integral inequalities for har- monically h-convex functions, U.P.B Sci. Bull. Serai A. 77 (2015), 5-16.
[21] J. E. Pečarič, F. Proschan, Y. L. Tong, Convex Functions, Partial Orderings and Statistical Applications, Mathe- matics in Science and Engineering, vol. 187, 1992.
[22] M. Z. Sarikaya, On new Hermite Hadamard Fejér type integral inequalities, Stud. Univ. BabeÅŸ-Bolyai Math. 57 (2012), no. 3, 377-386.
[23] Y. Shuang, H. P. Yin, F. Qi, Hermite-Hadamard type integral inequalities for geometric- arithmetically s-convex functions, Analysis 33 (2013), 1001-1010.