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ON NEW INEQUALITIES OF HERMITE-HADAMARD-FEJER TYPE FOR GA-s CONVEX FUNCTIONS VIA FRACTIONAL INTEGRALS

Year 2016, Volume: 4 Issue: 1, 130 - 139, 01.04.2016

Abstract

In this paper, some Hermite-Hadamard-Fejer type integral in- equalities for GA-s convex functions in fractional integral forms are obtained.

References

  • [1] L. Fejer, Uberdie Fourierreihen, II, Math. Naturwise. Anz Ungar. Akad., Wiss, 24 (1906), 369-390, (in Hungarian).
  • [2] J. Hadamard, Etude sur les proprietes des fonctions entieres et en particulier d'une fonction consideree par Riemann, J. Math. Pures Appl., 58 (1893), 171-215.
  • [3] _I. _ Iscan, Hermite-Hadamard-Fejer type inequalities for convex functions via fractional inte- grals, arXiv preprint arXiv:1404.7722 (2014).
  • [4] _I. _ Iscan, Generalization of di erent type integral inequalities for s-convex functions via frac- tional integrals, Applicable Analysis, 2013. doi: 10.1080/00036811.2013.851785.
  • [5] _I. _ Iscan, New general integral inequalities for quasi-geometrically convex functions via frac- tional integrals, J. Inequal. Appl., 2013(491) (2013), 15 pages.
  • [6] _I. _ Iscan, On generalization of di erent type integral inequalities for s-convex functions via fractional integrals, Mathematical Sciences and Applications E-Notes, 2(1) (2014), 55-67.
  • [7] A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and applications of fractional di erential equations, Elsevier, Amsterdam 2006.
  • [8] M. Kunt, _I. _ Iscan, On new inequalities of Hermite-Hadamard-Fejer type for GA-convex func- tions via fractional integrals, RGMIA Research Report Collection, 18(2015), Article 108, 12 pp.
  • [9] M. A. Latif, S. S. Dragomir and E. Momaniat, Some Fejer type integral inequalities for geometrically-arithmetically-convex functions with applications, RGMIA Research Report Collection, 18(2015), Article 25, 18 pp.
  • [10] C. P. Niculescu, Convexity according to the geometric mean, Math. Inequal. Appl. 3 (2) (2000), 155-167.
  • [11] C. P. Niculescu, Convexity according to means, Math. Inequal. Appl. 6 (4) (2003), 571-579.
  • [12] M.Z. Sarkaya, On new Hermite Hadamard Fejer type integral inequalities, Stud. Univ. Babes- Bolyai Math. 57(3) (2012), 377-386.
  • [13] Erhan Set, _I. _ Iscan, M. Zeki Sarikaya, M. Emin Ozdemir, On new inequalities of Hermite- Hadamard-Fejer type for convex functions via fractional integrals, Applied Mathematics and Computation, 259 (2015) 875-881.
  • [14] Y. Shuang, H. P. Yin, F. Qi, Hermite-Hadamard type integral inequalities for geometrically- arithmetically s-convex functions, Analysis (Munich) 33 (2) (2013) 197-208.
  • [15] K.-L. Tseng, G.-S. Yang and K.-C. Hsu, Some inequalities for di erentiable mappings and applications to Fejer inequality and weighted trapezoidal formula, Taiwanese journal of Math- ematics, 15(4) (2011), 1737-1747.
  • [16] J. Wang, X. Li, M. Feckan and Y. Zhou, Hermite-Hadamard-type inequalities for Riemann- Liouville fractional integrals via two kinds of convexity, Appl. Anal., 92(11) (2012), 2241-2253.
  • [17] J. Wang, C. Zhu and Y. Zhou, New generalized Hermite-Hadamard type inequalities and applications to special means, J. Inequal. Appl., 2013(325) (2013), 15 pages.
Year 2016, Volume: 4 Issue: 1, 130 - 139, 01.04.2016

Abstract

References

  • [1] L. Fejer, Uberdie Fourierreihen, II, Math. Naturwise. Anz Ungar. Akad., Wiss, 24 (1906), 369-390, (in Hungarian).
  • [2] J. Hadamard, Etude sur les proprietes des fonctions entieres et en particulier d'une fonction consideree par Riemann, J. Math. Pures Appl., 58 (1893), 171-215.
  • [3] _I. _ Iscan, Hermite-Hadamard-Fejer type inequalities for convex functions via fractional inte- grals, arXiv preprint arXiv:1404.7722 (2014).
  • [4] _I. _ Iscan, Generalization of di erent type integral inequalities for s-convex functions via frac- tional integrals, Applicable Analysis, 2013. doi: 10.1080/00036811.2013.851785.
  • [5] _I. _ Iscan, New general integral inequalities for quasi-geometrically convex functions via frac- tional integrals, J. Inequal. Appl., 2013(491) (2013), 15 pages.
  • [6] _I. _ Iscan, On generalization of di erent type integral inequalities for s-convex functions via fractional integrals, Mathematical Sciences and Applications E-Notes, 2(1) (2014), 55-67.
  • [7] A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and applications of fractional di erential equations, Elsevier, Amsterdam 2006.
  • [8] M. Kunt, _I. _ Iscan, On new inequalities of Hermite-Hadamard-Fejer type for GA-convex func- tions via fractional integrals, RGMIA Research Report Collection, 18(2015), Article 108, 12 pp.
  • [9] M. A. Latif, S. S. Dragomir and E. Momaniat, Some Fejer type integral inequalities for geometrically-arithmetically-convex functions with applications, RGMIA Research Report Collection, 18(2015), Article 25, 18 pp.
  • [10] C. P. Niculescu, Convexity according to the geometric mean, Math. Inequal. Appl. 3 (2) (2000), 155-167.
  • [11] C. P. Niculescu, Convexity according to means, Math. Inequal. Appl. 6 (4) (2003), 571-579.
  • [12] M.Z. Sarkaya, On new Hermite Hadamard Fejer type integral inequalities, Stud. Univ. Babes- Bolyai Math. 57(3) (2012), 377-386.
  • [13] Erhan Set, _I. _ Iscan, M. Zeki Sarikaya, M. Emin Ozdemir, On new inequalities of Hermite- Hadamard-Fejer type for convex functions via fractional integrals, Applied Mathematics and Computation, 259 (2015) 875-881.
  • [14] Y. Shuang, H. P. Yin, F. Qi, Hermite-Hadamard type integral inequalities for geometrically- arithmetically s-convex functions, Analysis (Munich) 33 (2) (2013) 197-208.
  • [15] K.-L. Tseng, G.-S. Yang and K.-C. Hsu, Some inequalities for di erentiable mappings and applications to Fejer inequality and weighted trapezoidal formula, Taiwanese journal of Math- ematics, 15(4) (2011), 1737-1747.
  • [16] J. Wang, X. Li, M. Feckan and Y. Zhou, Hermite-Hadamard-type inequalities for Riemann- Liouville fractional integrals via two kinds of convexity, Appl. Anal., 92(11) (2012), 2241-2253.
  • [17] J. Wang, C. Zhu and Y. Zhou, New generalized Hermite-Hadamard type inequalities and applications to special means, J. Inequal. Appl., 2013(325) (2013), 15 pages.
There are 17 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Mehmet Kunt

İmdat İşcan

Publication Date April 1, 2016
Submission Date July 10, 2014
Published in Issue Year 2016 Volume: 4 Issue: 1

Cite

APA Kunt, M., & İşcan, İ. (2016). ON NEW INEQUALITIES OF HERMITE-HADAMARD-FEJER TYPE FOR GA-s CONVEX FUNCTIONS VIA FRACTIONAL INTEGRALS. Konuralp Journal of Mathematics, 4(1), 130-139.
AMA Kunt M, İşcan İ. ON NEW INEQUALITIES OF HERMITE-HADAMARD-FEJER TYPE FOR GA-s CONVEX FUNCTIONS VIA FRACTIONAL INTEGRALS. Konuralp J. Math. April 2016;4(1):130-139.
Chicago Kunt, Mehmet, and İmdat İşcan. “ON NEW INEQUALITIES OF HERMITE-HADAMARD-FEJER TYPE FOR GA-S CONVEX FUNCTIONS VIA FRACTIONAL INTEGRALS”. Konuralp Journal of Mathematics 4, no. 1 (April 2016): 130-39.
EndNote Kunt M, İşcan İ (April 1, 2016) ON NEW INEQUALITIES OF HERMITE-HADAMARD-FEJER TYPE FOR GA-s CONVEX FUNCTIONS VIA FRACTIONAL INTEGRALS. Konuralp Journal of Mathematics 4 1 130–139.
IEEE M. Kunt and İ. İşcan, “ON NEW INEQUALITIES OF HERMITE-HADAMARD-FEJER TYPE FOR GA-s CONVEX FUNCTIONS VIA FRACTIONAL INTEGRALS”, Konuralp J. Math., vol. 4, no. 1, pp. 130–139, 2016.
ISNAD Kunt, Mehmet - İşcan, İmdat. “ON NEW INEQUALITIES OF HERMITE-HADAMARD-FEJER TYPE FOR GA-S CONVEX FUNCTIONS VIA FRACTIONAL INTEGRALS”. Konuralp Journal of Mathematics 4/1 (April 2016), 130-139.
JAMA Kunt M, İşcan İ. ON NEW INEQUALITIES OF HERMITE-HADAMARD-FEJER TYPE FOR GA-s CONVEX FUNCTIONS VIA FRACTIONAL INTEGRALS. Konuralp J. Math. 2016;4:130–139.
MLA Kunt, Mehmet and İmdat İşcan. “ON NEW INEQUALITIES OF HERMITE-HADAMARD-FEJER TYPE FOR GA-S CONVEX FUNCTIONS VIA FRACTIONAL INTEGRALS”. Konuralp Journal of Mathematics, vol. 4, no. 1, 2016, pp. 130-9.
Vancouver Kunt M, İşcan İ. ON NEW INEQUALITIES OF HERMITE-HADAMARD-FEJER TYPE FOR GA-s CONVEX FUNCTIONS VIA FRACTIONAL INTEGRALS. Konuralp J. Math. 2016;4(1):130-9.
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