Hermite-Hadamard-Fejér type inequalities for harmonically convex functions via fractional integrals
Year 2016,
Volume: 4 Issue: 3, 239 - 253, 30.09.2016
İmdat Iscan
Mehmet Kunt
,
Nazli Yazici
Abstract
In this paper, firstly, Hermite-Hadamard-Fejér type
inequality for harmonically convex functions in fractional integral forms have
been established. Secondly, an integral identity and some
Hermite-Hadamard-Fejér type integral inequalities for harmonically convex
functions in fractional integral forms have been obtained. The some results
presented here would provide extensions of those given in earlier works.
References
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- Z. Dahmani, On Minkowski and Hermite-Hadamard integral inequalities via fractional integration, Ann. Funct. Anal. 1(1) (2010), 51-58.
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- 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.
- İ. İşcan, S. Wu, Hermite-Hadamard type inequalities for harmonically convex functions via fractional integrals, Appl. Math. Comput., 238 (2014) 237-244.
- İ. İşcan, Hermite-Hadamard type inequalities for harmonically convex functions, Hacet. J. Math. Stat., 43 (6) (2014), 935-942
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- A. P. Prudnikov, Y. A. Brychkov, O. J. Marichev, Integral and series, Elementary Functions, vol. 1, Nauka, Moscow, 1981.
- M.Z. Sarıkaya, On new Hermite Hadamard Fejér type integral inequalities, Stud. Univ. Babeş-Bolyai Math. 57(3) (2012), 377–386.
- M.Z. Sarıkaya, E. Set, H. Yaldız and N. Başak, Hermite-Hadamard’s inequalities for fractional integrals and related fractional inequalities, Mathematical and Computer Modelling, 57(9) (2013), 2403-2407.
- 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.
- J. Wang, X. Li, M. Fečkan 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
- 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: 3, 239 - 253, 30.09.2016
İmdat Iscan
Mehmet Kunt
,
Nazli Yazici
References
- M. Bombardelli and S. Varošanec, Properties of h-convex functions related to the Hermite Hadamard Fejér inequalities, Computers and Mathematics with Applications 58 (2009), 1869 1877.
- F. Chen and S. Wu, Fejér and Hermite-Hadamard type inqequalities for harmonically convex functions, Jurnal of applied Mathematics, volume 2014, article id:386806.
- Z. Dahmani, On Minkowski and Hermite-Hadamard integral inequalities via fractional integration, Ann. Funct. Anal. 1(1) (2010), 51-58.
- L. Fejér, Uberdie Fourierreihen, II, Math. Naturwise. Anz Ungar. Akad., Wiss, 24 (1906), 369-390, (in Hungarian).
- 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.
- İ. İşcan, New estimates on generalization of some integral inequalities for s-convex functions and their applications, Int. J. Pure Appl. Math., 86(4) (2013), 727-746.
- İ. İşcan, Some new general integral inequalities for h-convex and h-concave functions, Adv. Pure Appl. Math. 5(1) (2014), 21-29 . doi: 10.1515/apam-2013-0029.
- İ. İşcan, Generalization of different type integral inequalitiesfor s-convex functions via fractional integrals, Applicable Analysis, 2013. doi: 10.1080/00036811.2013.851785.
- 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.
- İ. İşcan, S. Wu, Hermite-Hadamard type inequalities for harmonically convex functions via fractional integrals, Appl. Math. Comput., 238 (2014) 237-244.
- İ. İşcan, Hermite-Hadamard type inequalities for harmonically convex functions, Hacet. J. Math. Stat., 43 (6) (2014), 935-942
- A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and applications of fractional differential equations. Elsevier, Amsterdam (2006).
- M. A. Latif, S. S. Dragomir and E. Momoniat, Some Fejér type inequalities for harmonically-convex functions with applications to special means, http://rgmia.org/papers/v18/v18a24.pdf.
- A. P. Prudnikov, Y. A. Brychkov, O. J. Marichev, Integral and series, Elementary Functions, vol. 1, Nauka, Moscow, 1981.
- M.Z. Sarıkaya, On new Hermite Hadamard Fejér type integral inequalities, Stud. Univ. Babeş-Bolyai Math. 57(3) (2012), 377–386.
- M.Z. Sarıkaya, E. Set, H. Yaldız and N. Başak, Hermite-Hadamard’s inequalities for fractional integrals and related fractional inequalities, Mathematical and Computer Modelling, 57(9) (2013), 2403-2407.
- 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.
- J. Wang, X. Li, M. Fečkan 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
- 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.