Year 2016,
Volume: 4 Issue: 2, 102 - 109, 30.10.2016
Mehmet Kunt
,
İmdat İşcan
References
- es
[1] L. Fejér, Uber die Fourierreihen, II. Math. Naturwise. Anz Ungar. Akad., Wiss 24 (1906), 369-390, (in Hungarian).
- [2] J. Hadamard, Étude sur les propriétés des fonctions entières et en particulier d’une fonction considérée par
Riemann. J. Math. Pures Appl. 58 (1893), 171-215.
- [3] İ. İşcan, Hermite-Hadamard-Fejer type inequalities for convex functions via fractional integrals, arXiv preprint
arXiv:1404.7722 (2014).
- [4] İ. İşcan, Generalization of different type integral inequalities for s-convex functions via fractional integrals.
Applicable Analysis(2013), doi: 10.1080/00036811.2013.851785.
- [5] İ. İşcan, New general integral inequalities for quasi-geometrically convex functions via fractional integrals. J.
Inequal. Appl. (2013), 2013(491).
- [6] İ. İşcan, On generalization of different 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 differential equations. Elsevier.
Amsterdam, 2006.
- [8] M. Kunt, İ. İşcan, On new inequalities of Hermite-Hadamard-Fejer type for GA-convex functions 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 geometricallyarithmetically-convex
functions with applications. RGMIA Research Report Collection 18(2015), Article 25,18pp.
- [10] C. P. Niculescu, Convexity according to the geometric mean. Math. Inequal. Appl. 3 (2) (2000), 155-167. Available
online at http://dx.doi.org/10.7153/mia-03-19.
- [11] C. P. Niculescu, Convexity according to means. Math. Inequal. Appl. 6 (4) (2003), 571-579. Available online at
http://dx.doi.org/10.7153/mia-06-53.
- [12] M.Z. Sarıkaya, On new Hermite Hadamard Fejér type integral inequalities. Stud. Univ. Babe¸s-Bolyai Math. 57(3)
(2012), 377–386.
- [13] Erhan Set, İ. İşcan, 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] K.-L. Tseng, G.-S. Yang and K.-C. Hsu, Some inequalities for differentiable mappings and applications to Fejér
inequality and weighted trapezoidal formula. Taiwanese journal of Mathematics 15(4) (2011), 1737-1747.
- [15] 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. doi:10.1080/00036811.2012.727986.
- [16] J. Wang, C. Zhu and Y. Zhou, New generalized Hermite-Hadamard type inequalities and applications to special
means. J. Inequal. Appl. (2013), 2013(325), 15 pages.
On new inequalities of Hermite-Hadamard-Fejer type for quasi-geometrically convex functions via fractional integrals
Year 2016,
Volume: 4 Issue: 2, 102 - 109, 30.10.2016
Mehmet Kunt
,
İmdat İşcan
Abstract
In this paper, new Hermite-Hadamard-Fejer type integral inequalities for quasi-geometrically convex
functions in fractional integral forms are obtained.
References
- es
[1] L. Fejér, Uber die Fourierreihen, II. Math. Naturwise. Anz Ungar. Akad., Wiss 24 (1906), 369-390, (in Hungarian).
- [2] J. Hadamard, Étude sur les propriétés des fonctions entières et en particulier d’une fonction considérée par
Riemann. J. Math. Pures Appl. 58 (1893), 171-215.
- [3] İ. İşcan, Hermite-Hadamard-Fejer type inequalities for convex functions via fractional integrals, arXiv preprint
arXiv:1404.7722 (2014).
- [4] İ. İşcan, Generalization of different type integral inequalities for s-convex functions via fractional integrals.
Applicable Analysis(2013), doi: 10.1080/00036811.2013.851785.
- [5] İ. İşcan, New general integral inequalities for quasi-geometrically convex functions via fractional integrals. J.
Inequal. Appl. (2013), 2013(491).
- [6] İ. İşcan, On generalization of different 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 differential equations. Elsevier.
Amsterdam, 2006.
- [8] M. Kunt, İ. İşcan, On new inequalities of Hermite-Hadamard-Fejer type for GA-convex functions 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 geometricallyarithmetically-convex
functions with applications. RGMIA Research Report Collection 18(2015), Article 25,18pp.
- [10] C. P. Niculescu, Convexity according to the geometric mean. Math. Inequal. Appl. 3 (2) (2000), 155-167. Available
online at http://dx.doi.org/10.7153/mia-03-19.
- [11] C. P. Niculescu, Convexity according to means. Math. Inequal. Appl. 6 (4) (2003), 571-579. Available online at
http://dx.doi.org/10.7153/mia-06-53.
- [12] M.Z. Sarıkaya, On new Hermite Hadamard Fejér type integral inequalities. Stud. Univ. Babe¸s-Bolyai Math. 57(3)
(2012), 377–386.
- [13] Erhan Set, İ. İşcan, 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] K.-L. Tseng, G.-S. Yang and K.-C. Hsu, Some inequalities for differentiable mappings and applications to Fejér
inequality and weighted trapezoidal formula. Taiwanese journal of Mathematics 15(4) (2011), 1737-1747.
- [15] 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. doi:10.1080/00036811.2012.727986.
- [16] J. Wang, C. Zhu and Y. Zhou, New generalized Hermite-Hadamard type inequalities and applications to special
means. J. Inequal. Appl. (2013), 2013(325), 15 pages.