Have a personal or library account? Click to login
Inequalities of Hermite-Hadamard Type Cover
By: S. S. Dragomir  
Open Access
|Feb 2017

References

  1. [1] M. Alomari and M. Darus, The Hadamard’s inequality for s-convex function. Int. J. Math. Anal. (Ruse) 2 (2008), no. 13-16, 639-646.
  2. [2] M. Alomari and M. Darus, Hadamard-type inequalities for s-eonvex functions. Int. Math. Forum 3 (2008), no. 37-40, 1965-1975.
  3. [3] G. A. Anastassiou, Univariate Ostrowski inequalities, revisited. Monatsh. Math., 135 (2002), no. 3, 175-189.
  4. [4] N. S. Barnett, P. Cerone, S. S. Dragomir, M. R. Pinheiro,and A. Sofo, Ostrowski type inequalities for functions whose modulus of the derivatives are convex and applications. Inequality Theory and Applications, Vol. 2 (Chinju/Masan, 2001), 19-32, Nova Sci. Publ., Hauppauge, NY, 2003. Preprint:RGMIA Res. Rep. Coll. 5 (2002), No. 2, Art. 1 [Online http://rgmia.org/papers/v5n2/Paperwapp2q.pdf].
  5. [5] E. F. Beckenbach, Convex functions, Bull. Amer. Math. Soc. 54(1948), 439-460.10.1090/S0002-9904-1948-08994-7
  6. [6] M. Bombardelli and S. Varosanee, Properties of h-convex functions related to the Hermite-Hadamard-Fejer inequalities. Comput. Math. Appl. 58 (2009), no. 9, 1869-1877.
  7. [7] W. W. Breckner, Stetigkeitsaussagen für eine Klasse verallgemeinerter konvexer Funktionen in topologischen linearen Raumen. (German) Publ. Inst. Math. (Beograd) (N.S.) 23(37) (1978), 13-20.
  8. [8] W. W. Breckner and G. Orban, Continuity properties of rationally s-convex map¬pings with values in an ordered topological linear space. Universitatea ”Babe§- Bolyai”, Facultatea de Matematica, Cluj-Napoca, 1978. viii+92 pp.
  9. [9] P. Cerone and S. S. Dragomir, Midpoint-type rules from an inequalities point of view, Ed. G. A. Anastassiou, Handbook of Analytic-Computational Methods in Applied Mathematics, CRC Press, New York. 135-200.10.1201/9780429123610-4
  10. [10] P. Cerone and S. S. Dragomir, New bounds for the three-point rule involving the Ricmann-Stieltjes integrals, in Advances in Statistics Combinatorics and Related Areas, C. Gulati, et al. (Eds.), World Science Publishing, 2002, 53-62.10.1142/9789812776372_0006
  11. [11] P. Cerone, S. S. Dragomir and J. Roumeliotis, Some Ostrowski type inequalities for n-time differentiable mappings and applications, Demonstratio Mathematica, 32(2) (1999), 697-712.10.1515/dema-1999-0404
  12. [12] G. Cristescu, Hadamard type inequalities for convolution of h-convex functions. Ann. Tiberiu Popoviciu Semin. Funct. Equ. Approx. Convexity 8 (2010), 3-11.
  13. [13] S. S. Dragomir, Ostrowski’s inequality for monotonous mappings and applica¬tions, J. KSIAM, 3(1) (1999). 127-135.
  14. [14] S. S. Dragomir, The Ostrowski’s integral inequality for Lipschitzian mappings and applications, Comp. Math. Appl., 38 (1999), 33-37.10.1016/S0898-1221(99)00282-5
  15. [15] S. S. Dragomir, On the Ostrowski’s inequality for Riemann-Stieltjes integral, Korean J. Appl. Math., 7 (2000), 477-485.10.1007/BF03012263
  16. [16] S. S. Dragomir, On the Ostrowski’s inequality for mappings of bounded variation and applications, Math. Ineq. & Appl., 4(1) (2001), 33-40.10.7153/mia-04-05
  17. [17] S. S. Dragomir, On the Ostrowski inequality for Riemann-Stieltjes integral fb f (t) du (t) where / is of Holder type and u is of bounded variation and appli¬cations, J. KSIAM, 5(1) (2001), 35-45.
  18. [18] S. S. Dragomir, Ostrowski type inequalities for isotonic linear functionals, J. Inequal. Pure & Appl. Math., 3(5) (2002), Art. 68.
  19. [19] S. S. Dragomir, An inequality improving the first Hermite-Hadamard inequality for convex functions defined on linear spaces and applications for semi-inner products. J. Inequal. Pure Appl. Math. 3 (2002), no. 2, Article 31, 8 pp.
  20. [20] S. S. Dragomir, An inequality improving the first Hermite-Hadamard inequality for convex functions defined on linear spaces and applications for semi-inner products, J. Inequal. Pure Appl. Math. 3 (2002), No. 2, Article 31.
  21. [21] S. S. Dragomir, An inequality improving the second Hermite-Hadamard inequality for convex functions defined on linear spaces and applications for semi-inner products, J. Inequal. Pure Appl. Math. 3 (2002), No.3, Article 35.
  22. [22] S. S. Dragomir, An Ostrowski like inequality for convex functions and applications, Revista Math. Complutense, 16(2) (2003), 373-382.10.5209/rev_REMA.2003.v16.n2.16807
  23. [23] S. S. Dragomir, Operator Inequalities of Ostrowski and Trapezoidal Type. Springer Briefs in Mathematics. Springer, New York, 2012. x+112 pp. ISBN: 978-1-4614- 1778-110.1007/978-1-4614-1779-8_3
  24. [24] S. S. Dragomir, Bounds for the normalised Jensen functional, Bull. Austral. Math. Soc. 74 (2006), pp. 471-478.
  25. [25] S. S. Dragomir, P. Cerone, J. Roumeliotis and S. Wang, A weighted version of Ostrowski inequality for mappings of Hölder type and applications in numerical analysis, Bull. Math. Soc. Sci. Math. Romanie, 42(90) (4) (1999), 301-314.
  26. [26] S. S. Dragomir and S. Fitzpatrick, The Hadamard inequalities for s-convex functions in the second sense. Demonstratio Math. 32 (1999), no. 4, 687-696.
  27. [27] S. S. Dragomir and S. Fitzpatrick,The Jensen inequality for s-Breckner convex functions in linear spaces. Demonstratio Math. 33 (2000), no. 1, 43-49.
  28. [28] S. S. Dragomir and B. Mond, On Hadamard’s inequality for a class of functions of Godunova and Levin. Indian J. Math. 39 (1997), no. 1, 1-9.
  29. [29] S. S. Dragomir and C. E. M. Pearce, On Jensen’s inequality for a class of functions of Godunova and Levin. Period. Math. Hungar. 33 (1996), no. 2, 93-100.
  30. [30] S. S. Dragomir and C. E. M. Pearce, Quasi-convex functions and Hadamard’s inequality, Bull. Austral. Math. Soc. 57 (1998), 377-385.10.1017/S0004972700031786
  31. [31] S. S. Dragomir, J. Pečarić and L. Persson, Some inequalities of Hadamard type. Soochow J. Math. 21 (1995), no. 3, 335-341.
  32. [32] S. S. Dragomir, J. Pečarić and L. Persson, Properties of some functionals related to Jensen’s inequality, Acta Math. Hungarica, 70 (1996), 129-143.10.1007/BF00113918
  33. [33] S. S. Dragomir and Th. M. Rassias (Eds), Ostrowski Type Inequalities and Applications in Numerical Integration, Kluwer Academic Publisher, 2002. 10.1007/978-94-017-2519-4
  34. [34] S. S. Dragomir and S. Wang, A new inequality of Ostrowski’s type in L1−norm and applications to some special means and to some numerical quadrature rules, Tamkang J. of Math., 28 (1997), 239-244.10.5556/j.tkjm.28.1997.4320
  35. [35] S. S. Dragomir and S. Wang, Applications of Ostrowski’s inequality to the estimation of error bounds for some special means and some numerical quadrature rules, Appl. Math. Lett., 11 (1998), 105-109.10.1016/S0893-9659(97)00142-0
  36. [36] S. S. Dragomir and S. Wang, A new inequality of Ostrowski’s type in Lp−norm and applications to some special means and to some numerical quadrature rules, Indian J. of Math., 40(3) (1998), 245-304.
  37. [37] A. El Farissi, Simple proof and refinement of Hermite-Hadamard inequality, J. Math. Ineq. 4 (2010), No. 3, 365-369.
  38. [38] E. K. Godunova and V. I. Levin, Inequalities for functions of a broad class that contains convex, monotone and some other forms of functions. (Russian) Numer¬ical mathematics and mathematical physics (Russian), 138-142, 166, Moskov. Gos. Ped. Inst., Moscow, 1985
  39. [39] H. Hudzik and L. Maligranda, Some remarks on s-convex functions. Aequationes Math. 48 (1994), no. 1, 100-111.
  40. [40] E. Kikianty and S. S. Dragomir, Hermite-Hadamard’s inequality and the p-HH- norm on the Cartesian product of two copies of a normed space, Math. Inequal. Appl. (in press)
  41. [41] U. S. Kirmaci, M. Klaricic Bakula, M. E Özdemir and J. Pečarić , Hadamard- type inequalities for s-convex functions. Appl. Math. Comput. 193 (2007), no. 1, 26-35.
  42. [42] M. A. Latif, On some inequalities for h-convex functions. Int. J. Math. Anal. (Ruse) 4 (2010), no. 29-32, 1473-1482.
  43. [43] D. S. Mitrinović and I. B. Lackovic, Hermite and convexity, Aequationes Math. 28 (1985), 229-232.10.1007/BF02189414
  44. [44] D. S. Mitrinović and J. E. Pečarić , Note on a class of functions of Godunova and Levin. C. R. Math. Rep. Acad. Sci. Canada 12 (1990), no. 1, 33-36.
  45. [45] C. E. M. Pearce and A. M. Rubinov, P-functions, quasi-convex functions, and Hadamard-type inequalities. J. Math. Anal. Appl. 240 (1999), no. 1, 92-104.
  46. [46] J. E. Pečarić and S. S. Dragomir, On an inequality of Godunova-Levin and some refinements of Jensen integral inequality. Itinerant Seminar on Functional Equations, Approximation and Convexity (Cluj-Napoca, 1989), 263-268, Preprint, 89-6, Univ. ”Babe§-Bolyai”, Cluj-Napoca, 1989.
  47. [47] J. Pečarić and S. S. Dragomir, A generalization of Hadamard’s inequality for isotonic linear functionals, Radovi Mat. (Sarajevo) 7 (1991), 103-107.
  48. [48] M. Radulescu, S. Radulescu and P. Alexandrescu, On the Godunova-Levin-Schur class of functions. Math. Inequal. Appl. 12 (2009), no. 4, 853-862.
  49. [49] M. Z. Sarikaya, A. Saglam, and H. Yildirim, On some Hadamard-type inequalities for h-convex functions. J. Math. Inequal. 2 (2008), no. 3, 335-341.
  50. [50] E. Set, M. E. Ozdemir and M. Z. Sarikaya, New inequalities of Ostrowski’s type for s-convex functions in the second sense with applications. Facta Univ. Ser. Math. Inform. 27 (2012), no. 1, 67-82.
  51. [51] M. Z. Sarikaya, E. Set and M. E. Özdemir, On some new inequalities of Hadamard type involving h-convex functions. Acta Math. Univ. Comenian. (N.S.) 79 (2010), no. 2, 265-272.
  52. [52] M. Tunç, Ostrowski-type inequalities via h-convex functions with applications to special means. J. Inequal. Appl. 2013. 2013:326.10.1186/1029-242X-2013-326
  53. [53] S. Varošanec, On h-convexity. J. Math. Anal. Appl. 326 (2007), no. 1, 303 311.
Language: English
Page range: 1 - 21
Submitted on: Mar 16, 2015
Accepted on: Apr 15, 2015
Published on: Feb 4, 2017
Published by: Sciendo
In partnership with: Paradigm Publishing Services
Publication frequency: 3 issues per year

© 2017 S. S. Dragomir, published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.