Fractional Hermite-Hadamard type integral inequalities for functions whose modulus of the mixed derivatives are co-ordinated s-preinvex in the second sense

Meftah, Badreddine; Souahi, Abdourazek

doi:10.2478/aupcsm-2019-0006

Abstract

In this paper we establish some fractional Hermite-Hadamard type integral inequalities for functions whose modulus of the mixed derivatives are co-ordinated s-preinvex in the second sense.

References

[1] Alomari, M. and M. Darus. “The Hadamard’s inequality for s-convex function.” Int. J. Math. Anal. (Ruse) 2, no. 13-16 (2008): 639-646. Cited on 67 and 69.
Search in Google Scholar Back to article
[2] Ben-Israel, A. and B. Mond. “What is invexity?” J. Austral. Math. Soc. Ser. B 28, no. 1 (1986): 1-9. Cited on 67.10.1017/S0334270000005142
Search in Google Scholar Back to article
[3] Dragomir, S.S. “On the Hadamard’s inequality for convex functions on the coordinates in a rectangle from the plane.” Taiwanese J. Math. 5, no. 4 (2001): 775-788. Cited on 67 and 68.10.11650/twjm/1500574995
Search in Google Scholar Back to article
[4] Hanson, Morgan A. “On sufficiency of the Kuhn-Tucker conditions.” J. Math. Anal. Appl. 80, no. 2 (1981): 545-550. Cited on 67.10.1016/0022-247X(81)90123-2
Search in Google Scholar Back to article
[5] Kilbas, Anatoly A., Hari M. Srivastava and Juan J. Trujillo. Theory and applications of fractional differential equations. Vol. 204 of North-Holland Mathematics Studies. Amsterdam: Elsevier Science B.V., 2006. Cited on 70.
Search in Google Scholar Back to article
[6] Latif, M.A. and M. Alomari. “Hadamard-type inequalities for product two convex functions on the co-ordinates.” Int. Math. Forum 4, no. 45-48 (2009): 2327-2338. Cited on 67 and 69.
Search in Google Scholar Back to article
[7] Latif, M. A. and M. Alomari. “New inequalities of Ostrowski type for co-ordinated convex functions via fractional integrals.” J. Fract. Calc. Appl. 2, no. 9 (2012): 1-15. Cited on 67 and 70.
Search in Google Scholar Back to article
[8] Latif, M.A. and S.S. Dragomir. “Some Hermite-Hadamard type inequalities for functions whose partial derivatives in absolute value are preinvex on the coordinates.” Facta Univ. Ser. Math. Inform. 28, no. 3 (2013): 257-270. Cited on 67 and 70.
Search in Google Scholar Back to article
[9] Matłoka, Marian. “On some Hadamard-type inequalities for (h₁, h₂)-preinvex functions on the co-ordinates.” J. Inequal. Appl. 2013, (2013): art id. 227. Cited on 67 and 69.10.1186/1029-242X-2013-227
Search in Google Scholar Back to article
[10] Meftah, B., K. Boukerrioua and T. Chiheb. “New Hadamard’s inequality for (s₁, s₂)-preinvex functions on co-ordinates.” Kragujevac J. Math. 39, no. 2 (2015): 231-254. Cited on 67 and 70.10.5937/KgJMath1502231M
Search in Google Scholar Back to article
[11] Meftah, B. “Fractional Hermite-Hadamard type integral inequalities for functions whose modulus of derivatives are co-ordinated log-preinvex.” Punjab Univ. J. Math. (Lahore) 51, no. 2 (2019): 21-37. Cited on 67 and 71.10.2478/aupcsm-2019-0006
Search in Google Scholar Back to article
[12] Noor, M. A. (1994). Variational-like inequalities. Optimization 30 (4), 323–330. Cited on 67.10.1080/02331939408843995
Search in Google Scholar Back to article
[13] Noor, M.A. “Invex equilibrium problems.” J. Math. Anal. Appl. 302, no. 2 (2005): 463-475. Cited on 67.10.1016/j.jmaa.2004.08.014
Search in Google Scholar Back to article
[14] Pečarić, Josip E., Frank Proschan and Y.L. Tong. Convex functions, partial orderings, and statistical applications. Vol. 187 of Mathematics in Science and Engineering. Academic Boston, MA: Press, Inc., 1992. Cited on 67.
Search in Google Scholar Back to article
[15] Pini, Rita. “Invexity and generalized convexity.” Optimization 22, no. 4 (1991): 513-525. Cited on 67.10.1080/02331939108843693
Search in Google Scholar Back to article
[16] Sarikaya, M.Z. “On the Hermite-Hadamard-type inequalities for co-ordinated convex function via fractional integrals.” Integral Transforms Spec. Funct. 25, no. 2, (2014): 134-147. Cited on 67, 68, 71, 74, 76 and 79.10.1080/10652469.2013.824436
Search in Google Scholar Back to article
[17] Sarikaya, M.Z. et all. “New some Hadamard’s type inequalities for co-ordinated convex functions.” Tamsui Oxf. J. Inf. Math. Sci. 28, no. 2 (2012): 137-152. Cited on 67.
Search in Google Scholar Back to article
[18] Weir, T. and B. Mond. “Pre-invex functions in multiple objective optimization.” J. Math. Anal. Appl. 136, no. 1 (1988): 29-38. Cited on 67.10.1016/0022-247X(88)90113-8
Search in Google Scholar Back to article
[19] Yang, Xin Min and Duan Li. “On properties of preinvex functions.” J. Math. Anal. Appl. 256, no. 1 (2001): 229-241. Cited on 67.10.1006/jmaa.2000.7310
Search in Google Scholar Back to article

Fractional Hermite-Hadamard type integral inequalities for functions whose modulus of the mixed derivatives are co-ordinated s-preinvex in the second sense

Abstract

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