Some new integral inequalities of Hermite-Hadamard type for (log; (α;m))-convex functions on coordinates

Authors

  • Bo-Yan XI College of Mathematics Inner Mongolia University for Nationalities Tongliao City, 028043 Inner Mongolia Autonomous Region, China e-mail: baoyintu78@qq.com, baoyintu68@sohu.com, baoyintu78@imun.edu.cn https://orcid.org/0000-0003-4528-2331
  • Feng QI Department of Mathematics, School of Science Tianjin Polytechnic University Tianjin City, 300387, China; Institute of Mathematics Henan Polytechnic University Jiaozuo City, 454010, Henan Province, China e-mail: qifeng618@gmail.com, qifeng618@hotmail.com, qifeng618@qq.com

Keywords:

Co-ordinates, (log; (α;m))-convex functions on co-ordinates, Hermite-Hadamard's inequality.

Abstract

In the paper, the authors introduce a new concept "log; (α;m))-convex functions on the co-ordinates on the rectangle of the plane" and establish some new integral inequalities of Hermite-Hadamard type for (log; (α;m))-convex functions on the co-ordinates on the rectangle from the plane.

Mathematics Subject Classification (2010): 26A51, 26D15, 26D20, 26E60, 41A55.

References

Bai, R.-F., Qi, F., Xi, B.-Y., Hermite-Hadamard type inequalities for the m- and (α;m)-

logarithmically convex functions, Filomat, 27(2013), no. 1, 1-7.

Bai, S.-P., Wang, S.-H., Qi, F., Some Hermite-Hadamard type inequalities for n-time differentiable (α;m)-convex functions, J. Inequal. Appl., 2012:267, 11 pages.

Chun, L., Some new inequalities of Hermite-Hadamard type for (α 1;m1)-( α 2;m2)-convex functions on coordinates, J. Funct. Spaces, 2014(2014), Article ID 975950, 7 pages.

Dragomir, S.S., On the Hadamard's inequality for convex functions on the co-ordinates in a rectangle from the plane, Taiwanese J. Math., 5(2001), no. 4, 775-788.

Dragomir, S.S., Pearce, C.E.M., Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA Monographs, Victoria University (2000).

Dragomir, S.S., Toader, G., Some inequalities for m-convex functions, Studia Univ. Babes-Bolyai Math., 38(1993), no. 1, 21-28.

Bakula, M.K., Ozdemir, M.E., Pecaric, J., Hadamard type inequalities for m-convex and (α;m)-convex functions, J. Inequal. Pure Appl. Math., 9(2008), no. 4, Art. 96, 12 pages.

Toader, G., Some generalizations of the convexity, Proceedings of the Colloquium on Approximation and Optimization, Cluj-Napoca, 1985, 329-338.

Mihesan, V.G., A generalization of the convexity, Seminar on Functional Equations, Approx. Convex, Cluj-Napoca, 1993 (Romanian).

Qi, F., Wei, Z.-L., Yang, Q., Generalizations and refinements of Hermite-Hadamard's inequality, Rocky Mountain J. Math., 35(2005), no. 1, 235-251.

Qi, F., Xi, B.-Y., Some integral inequalities of Simpson type for GA-"-convex functions, Georgian Math. J., 20(2013), no. 4, 775-788.

Xi, B.-Y., Bai, R.-F., Qi, F., Hermite-Hadamard type inequalities for the m- and (α;m)-geometrically convex functions, Aequationes Math., 84(2012), no. 3, 261-269.

Xi, B.-Y., Qi, F., Some Hermite-Hadamard type inequalities for differentiable convex functions and applications, Hacet. J. Math. Stat., 42(2013), no. 3, 243-257.

Xi, B.-Y., Qi, F., Some integral inequalities of Hermite-Hadamard type for convex functions with applications to means, J. Funct. Spaces Appl., 2012(2012), Article ID 980438, 14 pages.

Xi, B.-Y., Qi, F., Integral inequalities of Simpson type for logarithmically convex functions, Adv. Stud. Contemp. Math., Kyungshang, 23(2013), no. 4, 559-566.

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Published

2015-12-30

How to Cite

XI, B.-Y., & QI, F. (2015). Some new integral inequalities of Hermite-Hadamard type for (log; (α;m))-convex functions on coordinates. Studia Universitatis Babeș-Bolyai Mathematica, 60(4), 509–525. Retrieved from https://studia.reviste.ubbcluj.ro/index.php/subbmathematica/article/view/5821

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