We establish some new fractional integral inequalities for differentiable convex functions and give several applications for the Beta-function.
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M. Alomari and M. Darus, “On the Hadamard’s inequality for log-convex functions on the coordinates,” J. Inequal. Appl., Article ID 283147, 13 p. (2009).
S. S. Dragomir, “Two mappings in connection to Hadamard’s inequalities,” J. Math. Anal. Appl., 167, 49–56 (1992).
S. S. Dragomir, “On the Hadamard’s inequality for convex on the coordinates in a rectangle from the plane,” Taiwan. J. Math., 5, No. 4, 775–788 (2001).
S. S. Dragomir and R. P. Agarwal, “Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula,” Appl. Math. Lett., 11, No. 5, 91–95 (1998).
S. S. Dragomir, Y.-J. Cho, and S.-S. Kim, “Inequalities of Hadamard’s type for Lipschitzian mappings and their applications,” J. Math. Anal. Appl., 245, 489–501 (2000).
L. Fejér, “Über die Fourierreihen, II,” Math. Naturwiss. Anz Ungar. Akad. Wiss., 24, 369–390 (1906).
J. Hadamard, “ Étude sur les propriétés des fonctions entières en particulier d’une fonction considérée par Riemann,” J. Math. Pures Appl. (9), 58, 171–215 (1893).
S.-R. Hwang, K.-C. Hsu, and K.-L. Tseng, “Hadamard-type inequalities for Lipschitzian functions in one and two variables with their applications,” J. Math. Anal. Appl., 405, 546–554 (2013).
S.-R. Hwang, K.-L. Tseng, and K.-C. Hsu, “New inequalities for fractional integrals and their applications,” Turk. J. Math., 40, 471–486 (2016).
U. S. Kirmaci, “Inequalities for differentiable mappings and applications to special means of real numbers and to midpoint formula,” Appl. Math. Comput., 147, 137–146 (2004).
U. S. Kirmaci and M. E. Ö zdemir, “On some inequalities for differentiable mappings and applications to special means of real numbers and to midpoint formula,” Appl. Math. Comput., 153, 361–368 (2004).
C. E. M. Pearce and J. Pečarić, “Inequalities for differentiable mappings with application to special means and quadrature formula,” Appl. Math. Lett., 13, No. 2, 51–55 (2000).
M. Z. Sarikaya, E. Set, H. Yaldiz, and N. Başak, “Hermite–Hadamard’s inequalities for fractional integrals and related fractional inequalities,” Math. Comput. Model., 57, 2403–2407 (2013).
K.-L. Tseng, S.-R. Hwang, and S. S. Dragomir, “Fejér-type inequalities (I),” J. Inequal. Appl., Article ID 531976, 7 p. (2010).
K.-L. Tseng, G.-S. Yang, and K.-C. Hsu, “On some inequalities of Hadamard’s type and applications,” Taiwan. J. Math., 13, No. 6, 1929–1948 (2009).
G.-S. Yang and K.-L. Tseng, “On certain integral inequalities related to Hermite–Hadamard inequalities,” J. Math. Anal. Appl., 239, 180–187 (1999).
G.-S. Yang and K.-L. Tseng, “Inequalities of Hadamard’s type for Lipschitzian mappings,” J. Math. Anal. Appl., 260, 230–238 (2001).
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 69, No. 3, pp. 407–425, March, 2017.
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Tseng, KL., Hsu, KC. New Fractional Integral Inequalities for Differentiable Convex Functions and Their Applications. Ukr Math J 69, 478–499 (2017). https://doi.org/10.1007/s11253-017-1376-9
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DOI: https://doi.org/10.1007/s11253-017-1376-9