Some weighted integral inequalities for differentiable h-preinvex functions

References

[1] H. Alzer, A superadditive property of Hadamard’s gamma function, Abh. Math. Semin. Univ. Hambg. 79 (2009), no. 1, 11–23. 10.1007/s12188-008-0009-5Suche in Google Scholar

[2] T. Antczak, Mean value in invexity analysis, Nonlinear Anal. 60 (2005), no. 8, 1473–1484. 10.1016/j.na.2004.11.005Suche in Google Scholar

[3] A. Barani, A. G. Ghazanfari and S. S. Dragomir, Hermite–Hadamard inequality for functions whose derivatives absolute values are preinvex, J. Inequal. Appl. 2012 (2012), Paper No. 247. 10.1186/1029-242X-2012-247Suche in Google Scholar

[4] S. S. Dragomir, Two mappings in connection to Hadamard’s inequalities, J. Math. Anal. Appl. 167 (1992), no. 1, 49–56. 10.1016/0022-247X(92)90233-4Suche in Google Scholar

[5] 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 (1998), no. 5, 91–95. 10.1016/S0893-9659(98)00086-XSuche in Google Scholar

[6] D.-Y. Hwang, Some inequalities for differentiable convex mapping with application to weighted trapezoidal formula and higher moments of random variables, Appl. Math. Comput. 217 (2011), no. 23, 9598–9605. 10.1016/j.amc.2011.04.036Suche in Google Scholar

[7] D.-Y. Hwang, Some inequalities for differentiable convex mapping with application to weighted midpoint formula and higher moments of random variables, Appl. Math. Comput. 232 (2014), 68–75. 10.1016/j.amc.2014.01.050Suche in Google Scholar

[8] İ. İscan, Hermite–Hadamard’s inequalities for preinvex function via fractional integrals and related fractional inequalities, Amer. J. Math. Anal. 1 (2013), no. 3, 33–38. Suche in Google Scholar

[9] U. S. Kırmacı, Inequalities for differentiable mappings and applications to special means of real numbers and to midpoint formula, Appl. Math. Comput. 147 (2004), no. 1, 137–146. 10.1016/S0096-3003(02)00657-4Suche in Google Scholar

[10] U. S. Kırmacı and M. E. Özdemir, On some inequalities for differentiable mappings and applications to special means of real numbers and to midpoint formula, Appl. Math. Comput. 153 (2004), no. 2, 361–368. 10.1016/S0096-3003(03)00637-4Suche in Google Scholar

[11] M. A. Latif, On Hermite–Hadamard type integral inequalities for n-times differentiable preinvex functions with applications, Stud. Univ. Babeş-Bolyai Math. 58 (2013), no. 3, 325–343. Suche in Google Scholar

[12] M. A. Latif, Inequalities of Hermite–Hadamard type for functions whose derivatives in absolute value are convex with applications, Arab J. Math. Sci. 21 (2015), no. 1, 84–97. 10.1016/j.ajmsc.2014.01.002Suche in Google Scholar

[13] M. A. Latif and S. S. Dragomir, New inequalities of Hermite–Hadamard type for functions whose derivatives in absolute value are convex with applications, Acta Univ. M. Belii Ser. Math. 2013 (2013), 24–39. Suche in Google Scholar

[14] M. A. Latif and S. S. Dragomir, Some Hermite–Hadamard type inequalities for functions whose partial derivatives in absolute value are preinvex on the co-ordinates, Facta Univ. Ser. Math. Inform. 28 (2013), no. 3, 257–270. Suche in Google Scholar

[15] M. A. Latif and S. S. Dragomir, Some weighted integral inequalities for differentiable preinvex and prequasiinvex functions with applications, J. Inequal. Appl. 2013 (2013), Paper No. 575. 10.1186/1029-242X-2013-575Suche in Google Scholar

[16] M. A. Latif and S. S. Dragomir, Generalization of Hermite–Hadamard type inequalities for n-times differentiable functions which are s-preinvex in the second sense with applications, Hacet. J. Math. Stat. 44 (2015), no. 4, 839–853. 10.15672/HJMS.2015449438Suche in Google Scholar

[17] M. A. Latif, S. S. Dragomir and E. Momoniat, Some weighted Hermite–Hadamard–Noor type inequalities for differentiable preinvex and quasi preinvex functions, Punjab Univ. J. Math. (Lahore) 47 (2015), no. 1, 57–72. Suche in Google Scholar

[18] A. Lupaş, A generalization of Hadamard inequalities for convex functions, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz. 544–576 (1976), 115–121. Suche in Google Scholar

[19] M. Matloka, On some Hadamard-type inequalities for (h1,h2)-preinvex functions on the co-ordinates, J. Inequal. Appl. 2013 (2013), Paper No. 227. 10.1186/1029-242X-2013-227Suche in Google Scholar

[20] M. Matloka, Inequalities for h-preinvex functions, Appl. Math. Comput. 234 (2014), 52–57. 10.1016/j.amc.2014.02.030Suche in Google Scholar

[21] M. Matloka, On some new inequalities for differentiable (h1,h2)-preinvex functions on the co-ordinates, Math. Stat. 2 (2014), no. 2, 6–14. 10.13189/ms.2014.020102Suche in Google Scholar

[22] M. A. Noor, Hermite–Hadamard integral inequalities for log-preinvex functions, J. Math. Anal. Approx. Theory 2 (2007), no. 2, 126–131. Suche in Google Scholar

[23] M. A. Noor, On Hadamard integral inequalities involving two log-preinvex functions, J. Inequal. Pure Appl. Math. 8 (2007), no. 3, Paper No. 75. Suche in Google Scholar

[24] C. E. M. Pearce and J. Pečarić, Inequalities for differentiable mappings with application to special means and quadrature formulae, Appl. Math. Lett. 13 (2000), no. 2, 51–55. 10.1016/S0893-9659(99)00164-0Suche in Google Scholar

[25] F. Qi, Z.-L. Wei and Q. Yang, Generalizations and refinements of Hermite–Hadamard’s inequality, Rocky Mountain J. Math. 35 (2005), no. 1, 235–251. 10.1216/rmjm/1181069779Suche in Google Scholar

[26] A. Saglam, H. Yıldırım and M. Z. Sarikaya, Some new inequalities of Hermite–Hadamard’s type, Kyungpook Math. J. 50 (2010), no. 3, 399–410. 10.5666/KMJ.2010.50.3.399Suche in Google Scholar

[27] M. Z. Sarikaya and N. Aktan, On the generalization of some integral inequalities and their applications, Math. Comput. Modelling 54 (2011), no. 9–10, 2175–2182. 10.1016/j.mcm.2011.05.026Suche in Google Scholar

[28] M. Z. Sarikaya, M. Avci and H. Kavurmaci, On some inequalities of Hermite–Hadamard type for convex functions, AIP Conf. Proc. 1309 (2010), 10.1063/1.3525218. 10.1063/1.3525218Suche in Google Scholar

[29] M. Z. Sarikaya, H. Bozkurt and N. Alp, On Hermite–Hadamard type integral inequalities for preinvex and log-preinvex functions, Contemp. Anal. Appl. Math. 1 (2013), no. 2, 237–252. Suche in Google Scholar

[30] S. Varošanec, On h-convexity, J. Math. Anal. Appl. 326 (2007), no. 1, 303–311. 10.1016/j.jmaa.2006.02.086Suche in Google Scholar

[31] S.-H. Wang and F. Qi, Hermite–Hadamard type inequalities for n-times differentiable and preinvex functions, J. Inequal. Appl. 2014 (2014), Paper No. 49. 10.1186/1029-242X-2014-49Suche in Google Scholar

[32] Y. Wang, B.-Y. Xi and F. Qi, Hermite–Hadamard type integral inequalities when the power of the absolute value of the first derivative of the integrand is preinvex, Matematiche (Catania) 69 (2014), no. 1, 89–96. 10.1186/1029-242X-2014-97Suche in Google Scholar

[33] T. Weir and B. Mond, Pre-invex functions in multiple objective optimization, J. Math. Anal. Appl. 136 (1988), no. 1, 29–38. 10.1016/0022-247X(88)90113-8Suche in Google Scholar

[34] S.-H. Wu, On the weighted generalization of the Hermite–Hadamard inequality and its applications, Rocky Mountain J. Math. 39 (2009), no. 5, 1741–1749. 10.1216/RMJ-2009-39-5-1741Suche in Google Scholar

[35] G.-S. Yang, D.-Y. Hwang and K.-L. Tseng, Some inequalities for differentiable convex and concave mappings, Comput. Math. Appl. 47 (2004), no. 2–3, 207–216. 10.1016/S0898-1221(04)90017-XSuche in Google Scholar