Hermite–Hadamard type inequalities for extended s-convex functions on the co-ordinates in a rectangle

• Autorzy: Xi B.-Y , Hua J. , Qi F.

Identyfikatory

DOI

10.1515/jaa-2014-0004

• Języki publikacji: EN

Abstrakty

EN

In the paper, the authors obtain some Hermite–Hadamard type integral inequalities for extended s-convex functions on the co-ordinates in a rectangle.

Słowa kluczowe

EN

coordinate; extended s-convex function; Hermite–Hadamard type integral inequality

PL

koordynacja; funkcje s-wypukłe; nierówność Hermite-Hadamarda

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2014
• Tom: Vol. 20, nr 1
• Strony: 29--39
• Opis fizyczny: Bibliogr. 21 poz.

Twórcy

autor

Xi B.-Y

• College of Mathematics, Inner Mongolia University for Nationalities, Tongliao City, Inner Mongolia Autonomous Region, 028043, P. R. China

autor

Hua J.

• College of Mathematics, Inner Mongolia University for Nationalities, Tongliao City, Inner Mongolia Autonomous Region, 028043, P. R. China
• Erenhot International College, Inner Mongolia Normal University, Erenhot City, Inner Mongolia Autonomous Region, 011100, P. R. China

autor

Qi F.

• Department of Mathematics, College of Science, Tianjin Polytechnic University, Tianjin City, 300387, P. R. China
• Institute of Mathematics, Henan Polytechnic University, Jiaozuo City, Henan Province, 454010, P. R. China

Bibliografia

• [1] M. Alomari and M. Darus, Co-ordinated s-convex function in the first sense with some Hadamard-type inequalities, Int. J. Contemp. Math. Sci. 3 (2008), no. 32, 1557-1567.
• [2] M. Alomari and M. Darus, Hadamard-type ineualities for s-convex functions, Jnt. Math. Forum 3 (2008), no. 40, 1965-1975.
• [3] M. Alomari and M. Darus, On co-ordinated s-convex functions, Int. Math. Forum 3 (2008), no. 40, 1977-1989.
• [4] M. Alomari and M. Darus, The Hadamard’s inequality for s-convex function of 2-variables on the co-ordinetes, Int. J. Math. Anal. (Ruse) 2 (2008), no. 13-16, 629-638.
• [5] R.-F. Bai, F. Qi and B.-Y. Xi, Hermite-Hadamard type inequalities for the m- and (α, mn)-logarithmically convex functions, Filomat 27 (2013), no. 1, 1-7.
• [6] S.-P. Bai, S.-H. Wang and F. Qi, Some Hermite-Hadamard type inequalities for n-time differentiable (α, m)-convex functions, J. Inequal. Appl. 2012 (2012), Article ID 267.
• [7] S.S. Dragomir, On 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.
• [8] S.S. Dragomir and C. E. M. Pearce, Selected Topics on Hermite-Hadamard Type Inequalities and Applications, RGMIA Monographs, Victoria University, Melbourne, 2000; available online at http://rgmia.org/monographs/hermite_hadamard.html.
• [9] H. Hudzik and L. Maligranda, Some remarks of s-convex functions, Aequationes Math. 48 (1994), no. 1, 100-111.
• [10] M.A. Latif and M. Alomari, Hadamard-type inequalities for product two convex functions on the co-ordinetes, Int. Math. Forum 4 (2009), no. 47, 2327-2338.
• [11] M. A. Latif and M. Alomari, On Hadmard-type inequalities for h-convex functions on the co-ordinates, Int. J. Math. Anal. (Ruse) 3 (2009), no. 33, 1645-1656.
• [12] M.A. Latif and S.S. Dragomir, On some new inequalities for differentiable co-ordinated convex functions, J. lnequal. Appl. 2012 (2012), Article ID 28.
• [13] J. Park, Generalizations of the Simpson-like type inequalities for coordinated s-convex mappings, Far East J. Math. Sci. 51 (2011), no. 2, 205-216.
• [14] J. Park, Generalizations of the Simpson-like type inequalities for co-ordinated s-convex mappings in the second sense, Far East J. Math. Sci. 2012 (2012), Article ID 715751.
• [15] 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.
• [16] S.-H. Wang, B.-Y. Xi and F. Qi, On Hermite-Hadamard type inequalities for (α, m)-convex functions, Int. J. Open Probl. Comput. Sci. Math. 5 (2012), no. 4, 47-56.
• [17] S.-H. Wang, B.-Y. Xi and F. Qi, Some new inequalities of Hermite-Hadamard type for n-time differentiable functions which are m-convex, Analysis (Munich) 32 (2012), no. 3, 247-262.
• [18] B.-Y. Xi, R.-F. Bai and F. Qi, Hermite-Hadamard type inequalities for them- and (a, m)-geometrically convex functions, Aequationes Math. 84 (2012), no. 3, 261-269.
• [19] B.-Y. Xi and F. Qi, Some integral inequalities of Hermite-Hadamard type for convex functions with applications to means, J. Funct. Spaces Appl. 2012 (2012), Article ID 980438.
• [20] B.-Y. Xi and F. Qi, Some inequalities of Hermite-Hadamard type for h-convex functions, Adv. lnequal. Appl. 2 (2013), no. 1, 1-15.
• [21] T.-Y. Zhang, A.-P. Ji and F. Qi, On integral inequalities of Hermite-Hadamard type for s-geometrically convex functions, Abstr. Appl. Anal. 2012 (2012), Article ID 560586.