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

Yıl 2016, Cilt: 4 Sayı: 2, 1 - 10, 01.03.2016

İmdat Iscan Sercan Turhan Selahattin Maden

Öz

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.

Anahtar Kelimeler

Harmoically-convex Hermite-Hadamard-Fejer type inequality

Kaynakça

  • 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.

Yıl 2016, Cilt: 4 Sayı: 2, 1 - 10, 01.03.2016

İmdat Iscan Sercan Turhan Selahattin Maden

Öz

Kaynakça

  • 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.
Toplam 16 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Articles
Yazarlar

İmdat Iscan

Sercan Turhan Bu kişi benim

Selahattin Maden Bu kişi benim

Yayımlanma Tarihi 1 Mart 2016
Yayımlandığı Sayı Yıl 2016 Cilt: 4 Sayı: 2

Kaynak Göster

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. Mart 2016;4(2):1-10.
Chicago Iscan, İmdat, Sercan Turhan, ve Selahattin Maden. “Some Hermite-Hadamard-Fejer Type Inequalities for Harmonically Convex Functions via Fractional Integral”. New Trends in Mathematical Sciences 4, sy. 2 (Mart 2016): 1-10.
EndNote Iscan İ, Turhan S, Maden S (01 Mart 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, ve S. Maden, “Some Hermite-Hadamard-Fejer type inequalities for harmonically convex functions via fractional integral”, New Trends in Mathematical Sciences, c. 4, sy. 2, ss. 1–10, 2016.
ISNAD Iscan, İmdat vd. “Some Hermite-Hadamard-Fejer Type Inequalities for Harmonically Convex Functions via Fractional Integral”. New Trends in Mathematical Sciences 4/2 (Mart 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 vd. “Some Hermite-Hadamard-Fejer Type Inequalities for Harmonically Convex Functions via Fractional Integral”. New Trends in Mathematical Sciences, c. 4, sy. 2, 2016, ss. 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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