Generalizations of some Integral Inequalities for Fractional Integrals

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Abstract

In this paper we give generalizations of the Hadamard-type inequalities for fractional integrals. As special cases we derive several Hadamard type inequalities.

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  • [1] Alomari M. Darus M. On the Hadamard’s inequality for log-convex functions on the coordinates J. Inequal. Appl. 2009 Article ID 283147 13 pp.

  • [2] Azócar A. Nikodem K. Roa G. Fejér-type inequalities for strongly convex functions Ann. Math. Sil. 26 (2012) 43-53.

  • [3] Azpeitia A.G. Convex functions and the Hadamard inequality Rev. Colombiana Mat. 28 (1994) 7-12.

  • [4] Díaz R. Pariguan E. On hypergeometric functions and Pochhammer k-symbol Divulg. Mat. 15 (2007) no. 2 179-192.

  • [5] Dragomir S.S. Two mappings in connection to Hadamard’s inequalities J. Math. Anal. Appl. 167 (1992) no. 1 49-56.

  • [6] Dragomir S.S. On some new inequalities of Hermite-Hadamard type for m-convex functions Tamkang J. Math. 33 (2002) no. 1 55-65.

  • [7] Dragomir S.S. Agarwal R.P. Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula Appl. Math. Lett. 11 (1998) no. 5 91-95.

  • [8] Dragomir S.S. Pearce C.E.M. Selected topics on Hermite-Hadamard inequalities and applications RGMIA Monographs Victoria University Melbourne 2000.

  • [9] Farid G. Rehman A.U. Zahra M. On Hadamard inequalities for k-fractional integrals Nonlinear Funct. Anal. Appl. 21 (2016) no. 3 463-478.

  • [10] Fejér L. Über die Fourierreihen II Math. Naturwiss. Anz. Ungar. Akad. Wiss. 24 (1906) 369-390 (in Hungarian).

  • [11] Gill P.M. Pearce C.E.M. Pecaric J. Hadamard’s inequality for r-convex functions J. Math. Anal. Appl. 215 (1997) no. 2 461-470.

  • [12] Iscan I. Hermite-Hadamard-Fejér type inequalities for convex functions via fractional integrals Stud. Univ. Babes-Bolyai Math. 60 (2015) no. 3 355-366.

  • [13] Kirmaci U.S. Klaricic Bakula M. Özdemir M.E. Pecaric J. Hadamard-type inequalities for s-convex functions Appl. Math. Comput. 193 (2007) no. 1 26-35.

  • [14] Klaricic Bakula M. Özdemir M.E. Pecaric J. Hadamard type inequalities for m- convex and (m)-convex functions JIPAM. J. Inequal. Pure Appl. Math. 9 (2008) no. 4 Article 96 12 pp.

  • [15] Klaricic Bakula M. Pecaric J. Note on some Hadamard-type inequalities JIPAM. J. Inequal. Pure Appl. Math. 5 (2004) no. 3 Article 74 9 pp.

  • [16] Lesnic D. Characterizations of the functions with bounded variation Proceedings of the International Conference on Theory and Applications of Mathematics and Informatics (ICTAMI 2003) Part A Acta Univ. Apulensis Math. Inform. 6 (2003) 47-54.

  • [17] Mubeen S. Habibullah G.M. k-fractional integrals and application Int. J. Contemp. Math. Sci. 7 (2012) no. 1-4 89-94.

  • [18] Sarikaya M.Z. Erden S. On the Hermite-Hadamard-Féjer type integral inequality for convex function Turkish J. Anal. Number Theory 2 (2014) no. 3 85-89.

  • [19] Sarikaya M.Z. Set E. Yaldiz H. Basak N. Hermite-Hadamard’s inequalities for fractional integrals and related fractional inequalities Math. Comput. Modelling 57 (2013) no. 9-10 2403-2407.

  • [20] Wang J. Zhu C. Zhou Y. New generalized Hermite-Hadamard type inequalities and applications to special means J. Inequal. Appl. 2013 Article ID 325 15 pp.

  • [21] Xiang R. Refinements of Hermite-Hadamard type inequalities for convex functions via fractional integrals J. Appl. Math. Inform. 33 (2015) no. 1-2 119-125.

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