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Some Hermite-Hadamard-Fejer type inequalities for harmonically convex functions via fractional integral

Year 2016, Volume: 4 Issue: 2, 1 - 10, 01.03.2016

İmdat Iscan Sercan Turhan Selahattin Maden

Abstract

In this paper, we gave the new general identity for differentiable functions. As a result of this identity some new and general inequalities for differentiable harmonically-convex functions are obtained.

Keywords

Harmoically-convex Hermite-Hadamard-Fejer type inequality

References

  • F. Chen and S. Wu, Hermite-Hadamard type inequalities for harmonically s-convex functions, Sci. World (2014), 7, Article ID 279158.
  • Z. Dahmani, On Minkowski and Hermite-Hadamard integral inequalities via fractional integration, Ann. Funct. Anal. 1(1) (2010), pp. 51-58.
  • S. S. Dragomir, Hermite Hadamard’ s type inequalities for convex functions of selfadjoint operators in Hilbert spaces, Linear Algebra Appl. 436 (2012), no.5, 1503-1515.
  • D-Y. Hwang, Some inequalities for differentiable convex mapping with application to weighted trapezoidal formula and higher moments of random variables, Applied Mathematics and Computation, 217 (2011), 9598-9605.
  • I. Iscan, M. Kunt, Fej´er and Hermite-Hadamard-Fej´er type inequalities for harmonically s-convex functions via Fractional Integrals, The Australian Journal of Mathematical Analysis and Applications, (2015), Vol: 12, 1 ,Article 10, pp 1-6.
  • I. Iscan, Hermite-Hadamard type inequalities for harmonically convex functions, Hacettepe Journal of Mathematics and Statistics 43 (6) (2014), 935-942.
  • I. Iscan, Ostrowski type inequalities for harmonically s-convex functions, Konuralp Jurnal of Mathematics, Volume 3, No 1 (2015), pp. 63-74.
  • I. Iscan, Some new general integral inequalities for h-convex and h-concave functions, Adv. Pure Appl. Math. 5(1) (2014), pp. 21-29 . doi: 10.1515/apam-2013-0029.
  • I. Iscan, Generalization of different type integral inequalitiesfor s-convex functions via fractional integrals, Applicable Analysis, 2013. doi: 10.1080/00036811.2013.851785.
  • I. Iscan, M. Kunt, Hermite-Hadamard-Fejer type inequalities for harmonically convex functions via fractional integrals, RGMIA Research Report Collection, 18(2015), Article 107, pp. 1-16.
  • I. Iscan, S. Wu Hermite-Hadamard type inequalities for harmonically-convex functions via fractional integrals, Applied Mathematics and Computation, 238 (2014), 237–244.
  • I, Iscan, S. Turhan, Generalized Hermite-Hadamard-Fejer type inequalities for GA-convex functions via Fractional integral, arXiv:1511.03308v1 [math.CA], 10 Nov 2015.
  • M.A. Latif, New Hermite Hadamard type integral inequalities for GA-convex functions with applications. Volume 34, Issue 4 (Nov 2014).
  • L. Fej´er, Uberdie Fourierreihen, II, Math. Naturwise. Anz. Ungar. Akad. , Wiss, 24 (1906), pp. 369-390, (in Hungarian)
  • M. Z. Sarıkaya, On new Hermite Hadamard Fej´er type integral inequalities, Stud. Univ. Babes¸-Bolyai Math., 57(3) (2012), pp. 377–386.
  • M. Z. Sarıkaya, E. Set, H. Yaldız and N. Bas¸ak, Hermite-Hadamard’s inequalities for fractional integrals and related fractional inequalities, Mathematical and Computer Modelling, 57(9) (2013), pp. 2403-2407.

Year 2016, Volume: 4 Issue: 2, 1 - 10, 01.03.2016

İmdat Iscan Sercan Turhan Selahattin Maden

Abstract

References

  • F. Chen and S. Wu, Hermite-Hadamard type inequalities for harmonically s-convex functions, Sci. World (2014), 7, Article ID 279158.
  • Z. Dahmani, On Minkowski and Hermite-Hadamard integral inequalities via fractional integration, Ann. Funct. Anal. 1(1) (2010), pp. 51-58.
  • S. S. Dragomir, Hermite Hadamard’ s type inequalities for convex functions of selfadjoint operators in Hilbert spaces, Linear Algebra Appl. 436 (2012), no.5, 1503-1515.
  • D-Y. Hwang, Some inequalities for differentiable convex mapping with application to weighted trapezoidal formula and higher moments of random variables, Applied Mathematics and Computation, 217 (2011), 9598-9605.
  • I. Iscan, M. Kunt, Fej´er and Hermite-Hadamard-Fej´er type inequalities for harmonically s-convex functions via Fractional Integrals, The Australian Journal of Mathematical Analysis and Applications, (2015), Vol: 12, 1 ,Article 10, pp 1-6.
  • I. Iscan, Hermite-Hadamard type inequalities for harmonically convex functions, Hacettepe Journal of Mathematics and Statistics 43 (6) (2014), 935-942.
  • I. Iscan, Ostrowski type inequalities for harmonically s-convex functions, Konuralp Jurnal of Mathematics, Volume 3, No 1 (2015), pp. 63-74.
  • I. Iscan, Some new general integral inequalities for h-convex and h-concave functions, Adv. Pure Appl. Math. 5(1) (2014), pp. 21-29 . doi: 10.1515/apam-2013-0029.
  • I. Iscan, Generalization of different type integral inequalitiesfor s-convex functions via fractional integrals, Applicable Analysis, 2013. doi: 10.1080/00036811.2013.851785.
  • I. Iscan, M. Kunt, Hermite-Hadamard-Fejer type inequalities for harmonically convex functions via fractional integrals, RGMIA Research Report Collection, 18(2015), Article 107, pp. 1-16.
  • I. Iscan, S. Wu Hermite-Hadamard type inequalities for harmonically-convex functions via fractional integrals, Applied Mathematics and Computation, 238 (2014), 237–244.
  • I, Iscan, S. Turhan, Generalized Hermite-Hadamard-Fejer type inequalities for GA-convex functions via Fractional integral, arXiv:1511.03308v1 [math.CA], 10 Nov 2015.
  • M.A. Latif, New Hermite Hadamard type integral inequalities for GA-convex functions with applications. Volume 34, Issue 4 (Nov 2014).
  • L. Fej´er, Uberdie Fourierreihen, II, Math. Naturwise. Anz. Ungar. Akad. , Wiss, 24 (1906), pp. 369-390, (in Hungarian)
  • M. Z. Sarıkaya, On new Hermite Hadamard Fej´er type integral inequalities, Stud. Univ. Babes¸-Bolyai Math., 57(3) (2012), pp. 377–386.
  • M. Z. Sarıkaya, E. Set, H. Yaldız and N. Bas¸ak, Hermite-Hadamard’s inequalities for fractional integrals and related fractional inequalities, Mathematical and Computer Modelling, 57(9) (2013), pp. 2403-2407.
There are 16 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

İmdat Iscan

Sercan Turhan This is me

Selahattin Maden This is me

Publication Date March 1, 2016
Published in Issue Year 2016 Volume: 4 Issue: 2

Cite

APA Iscan, İ., Turhan, S., & Maden, S. (2016). Some Hermite-Hadamard-Fejer type inequalities for harmonically convex functions via fractional integral. New Trends in Mathematical Sciences, 4(2), 1-10.
AMA Iscan İ, Turhan S, Maden S. Some Hermite-Hadamard-Fejer type inequalities for harmonically convex functions via fractional integral. New Trends in Mathematical Sciences. March 2016;4(2):1-10.
Chicago Iscan, İmdat, Sercan Turhan, and Selahattin Maden. “Some Hermite-Hadamard-Fejer Type Inequalities for Harmonically Convex Functions via Fractional Integral”. New Trends in Mathematical Sciences 4, no. 2 (March 2016): 1-10.
EndNote Iscan İ, Turhan S, Maden S (March 1, 2016) Some Hermite-Hadamard-Fejer type inequalities for harmonically convex functions via fractional integral. New Trends in Mathematical Sciences 4 2 1–10.
IEEE İ. Iscan, S. Turhan, and S. Maden, “Some Hermite-Hadamard-Fejer type inequalities for harmonically convex functions via fractional integral”, New Trends in Mathematical Sciences, vol. 4, no. 2, pp. 1–10, 2016.
ISNAD Iscan, İmdat et al. “Some Hermite-Hadamard-Fejer Type Inequalities for Harmonically Convex Functions via Fractional Integral”. New Trends in Mathematical Sciences 4/2 (March 2016), 1-10.
JAMA Iscan İ, Turhan S, Maden S. Some Hermite-Hadamard-Fejer type inequalities for harmonically convex functions via fractional integral. New Trends in Mathematical Sciences. 2016;4:1–10.
MLA Iscan, İmdat et al. “Some Hermite-Hadamard-Fejer Type Inequalities for Harmonically Convex Functions via Fractional Integral”. New Trends in Mathematical Sciences, vol. 4, no. 2, 2016, pp. 1-10.
Vancouver Iscan İ, Turhan S, Maden S. Some Hermite-Hadamard-Fejer type inequalities for harmonically convex functions via fractional integral. New Trends in Mathematical Sciences. 2016;4(2):1-10.
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