On Some Hadamard-Type Inequalities for Product of Two h-Convex Functions On the Co-ordinates

On Some Hadamard-Type Inequalities for Product of Two h-Convex Functions On the Co-ordinates

In this paper, Hadamard-type inequalities for product of h-convex functions on the co-ordinates on the rectangle from the plane are established. Obtained results generalize the corresponding to some well-known results given before now.

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  • M. Alomari and M. Darus, The Hadamard’s inequality for convex function of variables on the co-ordinates, Int. Journal of Math. Analysis, 2 (13) (2008), 629–638.
  • M. Alomari and M. Darus, The Hadamard’s inequality for convex function, Int. Journal of Math. Analysis, 2 (13) (2008), 639–646.
  • M. Alomari and M. Darus, On co–ordinated convex functions, International Mathematical Forum, 3, 2008, no. 40, 1977 - 1989.
  • M. Alomari and M. Darus, Co-ordinates convex function in the first sense with some Hadamard-type inequalities, Int. J. Contemp. Math. Sci., 32, 2008, 1557-1567.
  • M. Alomari and M. Darus, Hadamard-Type Inequalities for convex functions, International Mathematical Forum, 3, 2008, no. 40, 1965 - 1975.
  • W.W. Breckner, Stetigkeitsaussagen für eine Klasse verallgemeinerter konvexer funktionen in topologischen linearen Raumen, Pupl. Inst. Math., 23 (1978), 13–20.
  • W.W. Breckner, Continuity of generalized convex and generalized concave set-valued functions, Rev Anal. Numér. Thkor. Approx., 22 (1993), 39–51.
  • S.S. Dragomir, On Hadamard’s inequality for convex functions on the co-ordinates in a rectangle from the plane, Taiwanese Journal of Mathematics, 5 (2001), 775 - 788.
  • SS. Dragomir and S. Fitzpatrick, The Hadamard’s inequality for convex functions in the second sense, Demonstratio Math., 32 (4) (1999), 687–696.
  • S.S. Dragomir, J. Pecaric and L.E. Persson, Some inequalities of Hadamard type, Soochow J. Math., 21 (1995), 335–241.
  • E.K. Godunova and V.I. Levin, Neravenstva dlja funkcii sirokogo klassa, soderzascego vypuklye, monotonnye i nekotorye drugie vidy funkii, Vycislitel. Mat. i. Fiz. Mezvuzov. Sb. Nauc. Trudov, MGPI, Moskva, 1985, pp. 138–142.
  • H. Hudzik and L. Maligranda, Some remarks on convex functions, Aequationes Math., 48 (1994), 100–111.
  • U.S. Kırmacı, M.K. Bakula, M.E. Özdemir and J. Pecaric, Hadamard-type inequalities for convex functions, Appl. Math. and Compt., 193 (2007), 26–35.
  • M.A. Latif and M. Alomari, On Hadamard-type inequalities of product of two convex functions on the co-ordinates, International Mathematical Forum, 4 (2009), no. 47, 2327-2338.
  • D.S. Mitrinovic and J. Pecaric, Note on a class of functions of Godunova and Levin, C. R. Math. Rep. Acad. Sci. Can., 12 (1990), 33–36.
  • D.S. Mitrinovic, J. Pecaric and A.M. Fink, Classical and new inequalities in analysis, Kluwer Academic, Dordrecht, 1993.
  • B.G. Pachpatte, On some inequalities for convex functions, RGMIA Res. Rep. Coll., 6 (E), 2003.
  • M.Z Sarıkaya, A. Sağlam and H. Yıldırım, On some Hadamard-type inequalities for convex functions, Journal of Math. Ineq., Vol. 2, Number 3 (2008), 335-341.
  • S. Varosanec, On convexity, J. Math. Anal. Appl., 326 (2007), 303-311.
  • M.Z. Sarıkaya, E. Set and M.E. Özdemir, On some new inequalities of Hadamard type involving convex functions, Acta Math. Univ. Comenianae, LXXIX., 2 (2010), 265-272.
  • M.E. Özdemir, E. Set, M.Z. Sarıkaya, Some new Hadamard’s type inequalities for co-ordinated convex and
  • ( convex functions, Hacettepe J. of. Math. and Ist., 40, 219-229, (2011).
  • M.Z. Sar kaya, E. Set, M.E. Özdemir and S.S. Dragomir, New some Hadamard’s type inequalities for co-ordinated convex functions, Accepted.
  • M.A. Latif and M. Alomari, On Hadamard-type inequalities for convex functions on the co-ordinates, Int. Journal of Math. Analysis, 33, 2009, 1645-1656.
  • M. K. Bakula, M. E. Özdemir and J. Pecaric, Hadamard-type inequalities for convex and convex functions, J. Inequal. Pure and Appl. Math., 9, (4), (2007), Article 96