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Fractional Hermite-Hadamard type inequalities for co-ordinated prequasiinvex functions

 and    | Jun 22, 2019

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Ben-Israel, A. and Mond, B. 1986. What is invexity? J. Austral. Math. Soc. Ser. B 28, 1, 1–9.10.1017/S0334270000005142Search in Google Scholar

Dragomir, S. S. 2001. On the Hadamard’s inequality for convex functions on the co-ordinates in a rectangle from the plane. Taiwanese J. Math. 5, 4, 775–788.10.11650/twjm/1500574995Search in Google Scholar

Hanson, M. A. 1981. On sufficiency of the Kuhn-Tucker conditions. J. Math. Anal. Appl. 80, 2, 545–550.10.1016/0022-247X(81)90123-2Search in Google Scholar

Kilbas, A. A., Srivastava, H. M., and Trujillo, J. J. 2006. Theory and applications of fractional differential equations. North-Holland Mathematics Studies, vol. 204. Elsevier Science B.V., Amsterdam.Search in Google Scholar

Latif, M. A. and Dragomir, S. S. 2013. 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, 3, 257–270.Search in Google Scholar

Matł Oka, M. 2013. On some Hadamard-type inequalities for (h1, h2)-preinvex functions on the co-ordinates. J. Inequal. Appl., 2013:227, 12.10.1186/1029-242X-2013-227Search in Google Scholar

Meftah, B. 2019. Fractional hermite-hadamard type integral inequalities for functions whose modulus of derivatives are co-ordinated log-preinvex. Punjab Univ. J. Math. (Lahore) 51, 2.10.36753/mathenot.618335Search in Google Scholar

Noor, M. A. 1994. Variational-like inequalities. Optimization 30, 4, 323–330.10.1080/02331939408843995Search in Google Scholar

Noor, M. A. 2005. Invex equilibrium problems. J. Math. Anal. Appl. 302, 2, 463–475.10.1016/j.jmaa.2004.08.014Search in Google Scholar

Özdemir, M. E., Akdemir, A. O., and Yi Ldiz, C. 2012. On co-ordinated quasi-convex functions. Czechoslovak Math. J. 62(137), 4, 889–900.10.1007/s10587-012-0072-zSearch in Google Scholar

Özdemir, M. E., Yi Ldiz, C., and Akdemir, A. O. 2012. On some new Hadamard-type inequalities for co-ordinated quasi-convex functions. Hacet. J. Math. Stat. 41, 5, 697–707.10.1186/1029-242X-2012-21Search in Google Scholar

Pečarić, J. E., Proschan, F., and Tong, Y. L. 1992. Convex functions, partial orderings, and statistical applications. Mathematics in Science and Engineering, vol. 187. Academic Press, Inc., Boston, MA.Search in Google Scholar

Pini, R. 1991. Invexity and generalized convexity. Optimization 22, 4, 513–525.10.1080/02331939108843693Search in Google Scholar

Sari Kaya, M. Z. 2014. On the Hermite-Hadamard-type inequalities for co-ordinated convex function via fractional integrals. Integral Transforms Spec. Funct. 25, 2, 134–147.10.1080/10652469.2013.824436Search in Google Scholar

Weir, T. and Mond, B. 1988. Pre-invex functions in multiple objective optimization. J. Math. Anal. Appl. 136, 1, 29–38.10.1016/0022-247X(88)90113-8Search in Google Scholar

Yang, X. M. and Li, D. 2001. On properties of preinvex functions. J. Math. Anal. Appl. 256, 1, 229–241.10.1006/jmaa.2000.7310Search in Google Scholar

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