Some integral inequalities of the HermiteHadamard type for logconvex functions on coordinates

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Authors
YuMei Bai
 College of Mathematics, Inner Mongolia University for Nationalities, Tongliao City, Inner Mongolia Autonomous Region, China.
Feng Qi
 Department of Mathematics, College of Science, Tianjin Polytechnic University, Tianjin City, 300160, China.
 Institute of Mathematics, Henan Polytechnic University, Jiaozuo City, Henan Province, 454010, China.
Abstract
In the paper, the authors establish some new integral inequalities for logconvex functions on coordinates.
These newlyestablished inequalities are connected with integral inequalities of the HermiteHadamard type
for logconvex functions on coordinates.
Keywords
 Logconvex functions
 coordinates
 integral inequality
 HermiteHadamard type.
MSC
 26A51
 26D15
 26D20
 26E60
 41A55
References

[1]
M. Alomari, M. Darus, On the Hadamard's inequality for logconvex functions on the coordinates, J. Inequal. Appl., 2009 (2009), 13 pages

[2]
S.P. Bai, F. Qi, S.H. Wang, Some new integral inequalities of HermiteHadamard type for (\(\alpha,m,P\))convex functions on coordinates, J. Appl. Anal. Comput., 6 (2016), 171178

[3]
S. S. Dragomir, On the Hadamards inequlality for convex functions on the coordinates in a rectangle from the plane, Taiwanese J. Math., 5 (2001), 775788

[4]
S. S. Dragomir, C. E. M. Pearce, Selected topics on HermiteHadamard inequalities and applications, RGMIA Monographs, Victoria University (2002)

[5]
P. M. Gill, C. E. M. Pearce, J. Pečarić, Hadamard's inequality for rconvex functions, J. Math. Anal. Appl., 215 (1997), 461470

[6]
X.Y. Guo, F. Qi, B.Y. Xi, Some new inequalities of HermiteHadamard type for geometrically mean convex functions on the coordinates, J. Comput. Anal. Appl., 21 (2016), 144155

[7]
D.Y. Hwang, K.L. Tseng, G.S. Yang, Some Hadamard's inequalities for coordinated convex functions in a rectangle from the plane, Taiwanese J. Math., 11 (2007), 6373

[8]
M. Klaričić Bakula, J. Pečarić, On the Jensen's inequality for convex functions on the coordinates in a rectangle from the plane, Taiwanese J. Math., 10 (2006), 12711292

[9]
M. E. Özdemir, A. O. Akdemir, H. Kavurmacı, On the Simpsons inequality for coordinated convex functions, Turkish J. Anal. Number Theory, 2 (2014), 165169

[10]
M. E. Özdemir, A. O. Akdemir, Ç . Yıldız, On coordinated quasiconvex functions, Czechoslovak Math. J., 62 (2012), 889900

[11]
M. E. Özdemir, E. Set, M. Z. Sarikaya, Some new Hadamard type inequalities for coordinated mconvex and (\(\alpha,m\))convex functions, Hacet. J. Math. Stat., 40 (2011), 219229

[12]
M. E. Özdemir, Ç . Yıldız, A. O. Akdemir, On some new Hadamardtype inequalities for coordinated quasiconvex functions, Hacet. J. Math. Stat., 41 (2012), 697707

[13]
F. Qi, B.Y. Xi, Some integral inequalities of Simpson type for \(GA\varepsilon\)convex functions, Georgian Math. J., 20 (2013), 775788

[14]
M. Z. Sarikaya, On the HermiteHadamardtype inequalities for coordinated convex function via fractional integrals, Integral Transforms Spec. Funct., 25 (2014), 134147

[15]
M. Z. Sarikaya, Some inequalities for differentiable coordinated convex mappings, AsianEur. J. Math., 8 (2015), 21 pages

[16]
M. Z. Sarikaya, H. Budak, H. Yaldiz, Čebyševtype inequalities for coordinated convex functions, Pure Appl. Math. Lett., 2 (2014), 3640

[17]
M. Z. Sarikaya, H. Budak, H. Yaldiz, Some new Ostrowski type inequalities for coordinated convex functions, Turkish J. Anal. Number Theory, 2 (2014), 176182

[18]
M. Z. Sarikaya, E. Set, M. E. Ozdemir, S. S. Dragomir, New some Hadamard's type inequalities for coordinated convex functions, Tamsui Oxf. J. Inf. Math. Sci., 28 (2012), 137152

[19]
E. Set, M. Z. Sarikaya, A. O. Akdemir, Hadamard type inequalities for \(\varphi\)convex functions on coordinates, Tbilisi Math. J., 7 (2014), 5160

[20]
E. Set, M. Z. Sarikaya, H. Ögülmüş, Some new inequalities of HermiteHadamard type for hconvex functions on the coordinates via fractional integrals, Facta Univ. Ser. Math. Inform., 29 (2014), 397414

[21]
S.H. Wang, F. Qi, HermiteHadamard type inequalities for sconvex functions via RiemannLiouville fractional integrals, J. Comput. Anal. Appl., 22 (2017), 11241134

[22]
Y. Wang, B.Y. Xi, F. Qi, Integral inequalities of HermiteHadamard type for functions whose derivatives are strongly \(\alpha\)preinvex, Acta Math. Acad. Paedagog. Nyházi. (N.S.), 32 (2016), 7987

[23]
Y. Wu, F. Qi,, On some HermiteHadamard type inequalities for (s;QC)convex functions, SpringerPlus, 5 (2016), 13 pages

[24]
B.Y. Xi, F. Qi, Integral inequalities of Simpson type for logarithmically convex functions, Adv. Stud. Contemp. Math. (Kyungshang), 23 (2013), 559566

[25]
J. Zhang, F. Qi, G.C. Xu, Z.L. Pei, HermiteHadamard type inequalities for ntimes differentiable and geometrically quasiconvex functions, SpringerPlus, 5 (2016), 6 pages