Ir al contenido

Documat

Companions of Hermite-Hadamard Inequality for Convex Functions (II)

  • Dragomir, S. S. [1] ; Gomm, I. [1]
    1. [1] Victoria University

      Victoria University

      Australia

  • Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 33, Nº. 4, 2014, págs. 349-367
  • Idioma: inglés
  • DOI: 10.4067/S0716-09172014000400001
  • Enlaces
  • Resumen

    • Companions of Hermite-Hadamard inequalities for convex functions defined on the positive axis in the case when the integral has either the weight ψ or 1 ,t > 0 are given. Applications for special means are provided as well.

  • Referencias bibliográficas
    • Citas [1] G. ALLASIA, C. GIORDANO, J. PECARIC, Hadamard-type inequalities for (2r)-convex functions with applications, Atti Acad. Sci.‏...
    • [2] H. ALZER, A note on Hadamard’s inequalities, C.R. Math. Rep. Acad.‏ Sci. Canada, 11, pp. 255-258, (1989).‏
    • [3] H. ALZER, On an integral inequality, Math. Rev. Anal. Numer. Theor.‏ Approx., 18, pp. 101-103, (1989).‏
    • [4] A. G. AZPEITIA, Convex functions and the Hadamard inequality,‏ Rev.-Colombiana-Mat., 28 (1), pp. 7—12, (1994).‏
    • [5] D. BARBU, S. S. DRAGOMIR and C. BUS ¸E, A probabilistic argument for the convergence of some sequences associated to Hadamard’s‏ inequality,...
    • [6] C. BUSE, S. S. DRAGOMIR and D. BARBU, The convergence of some‏ sequences connected to Hadamard’s inequality, Demostratio Math., 29‏ (1),...
    • [7] S. S. DRAGOMIR, A mapping in connection to Hadamard’s inequalities, An. Oster. Akad. Wiss. Math.-Natur., (Wien), 128, pp. 17-20.‏ MR 934:26032....
    • [8] S. S. DRAGOMIR, A refinement of Hadamard’s inequality for isotonic‏ linear functionals, Tamkang J. of Math. (Taiwan), 24 , pp. 101-106.‏...
    • [9] S. S. DRAGOMIR, On Hadamard’s inequalities for convex functions,‏ Mat. Balkanica, 6, pp. 215-222. MR: 934, (1992). 26033.‏
    • [10] S. S. DRAGOMIR, On Hadamard’s inequality for the convex mappings‏ defined on a ball in the space and applications, Math. Ineq. &...
    • [11] S. S. DRAGOMIR, On Hadamard’s inequality on a disk, Journal of Ineq. in Pure & Appl. Math., 1, No. 1, Article 2,‏ http://jipam.vu.edu.au/,...
    • [12] S. S. DRAGOMIR, Some integral inequalities for differentiable convex‏ functions, Contributions, Macedonian Acad. of Sci. and Arts, 13...
    • [13] S. S. DRAGOMIR, Some remarks on Hadamard’s inequalities for convex functions, Extracta Math., 9 (2), pp. 88-94, (1994).‏
    • [14] S.S. DRAGOMIR, Two mappings in connection to Hadamard’s inequalities, J. Math. Anal. Appl., 167, pp. 49-56. MR:934:26038, ZBL‏ No. 758:26014,...
    • [15] S. S. DRAGOMIR, , An inequality improving the first HermiteHadamard inequality for convex functions defined on linear spaces and‏ applications...
    • [16] S. S. DRAGOMIR, An inequality improving the second HermiteHadamard inequality for convex functions defined on linear spaces and‏ applications...
    • [17] S.S. DRAGOMIR and R. P. AGARWAL, Two new mappings associated with Hadamard’s inequalities for convex functions, Appl. Math.‏ Lett., 11,...
    • [18] S. S. DRAGOMIR and C. BUSE, Refinements of Hadamard’s inequality for multiple integrals, Utilitas Math (Canada), 47, pp. 193-195,‏ (1995).‏
    • [19] S. S. DRAGOMIR, Y. J. CHO and S. S. KIM, Inequalities of‏ Hadamard’s type for Lipschitzian mappings and their applications,‏ J. of Math....
    • [20] S. S. DRAGOMIR and I. GOMM, Bounds for two mappings associated‏ to the Hermite-Hadamard inequality, Aust. J. Math. Anal. Appl., 8,‏ Art....
    • [21] S. S. DRAGOMIR and I. GOMM, Some new bounds for two mappings related to the Hermite-Hadamard inequality for convex functions, Num. Alg....
    • [22] S. S. DRAGOMIR and I. GOMM, Companions of Hermite-Hadamard‏ Inequality for Convex Functions (I), Preprint RGMIA Res. Rep. Coll.,‏ 17...
    • [23] S. S. DRAGOMIR and S. FITZPATRICK, The Hadamard’s inequality‏ for s-convex functions in the first sense, Demonstratio Math., 31 (3),‏...
    • [24] S. S. DRAGOMIR and S. FITZPATRICK, The Hadamard’s inequality‏ for s-convex functions in the second sense, Demonstratio Math., 32‏ (4),...
    • [25] S. S. DRAGOMIR and N. M. IONESCU, On some inequalities for‏ convex-dominated functions, Anal. Num. Theor. Approx., 19, pp. 21-28. MR...
    • [26] S. S. DRAGOMIR, D. S. MILOSEVIC and J. SANDOR, On some refinements of Hadamard’s inequalities and applications, Univ. Belgrad,‏ Publ....
    • [27] S.S. DRAGOMIR and B. MOND, On Hadamard’s inequality for a‏ class of functions of Godunova and Levin, Indian J. Math., 39, No. 1,‏ pp....
    • [28] S. S. DRAGOMIR and C. E. M. PEARCE, Quasi-convex functions‏ and Hadamard’s inequality, Bull. Austral. Math. Soc., 57 , pp. 377-385, (1998).‏
    • [29] S.‏ S. DRAGOMIR and C. E. M. PEARCE, Selected Topics on HermiteHadamard Inequalities and Applications, RGMIA Monographs, (2000).‏ [Online...
    • [30] S. S. DRAGOMIR, C. E. M. PEARCE and J. E. PECARIC, On Jessen’s and related inequalities for isotonic sublinear functionals, Acta‏ Math....
    • [31] S. S. DRAGOMIR, J. E. PECARIC and L. E. PERSSON, Some inequalities of Hadamard type, Soochow J. of Math. (Taiwan), 21, pp.‏ 335-341,...
    • [32] S. S. DRAGOMIR, J. E. PECARIC and J. SANDOR, A note on the Jensen-Hadamard inequality, Anal. Num. Theor. Approx., 19, pp. 21-28. MR 93b...
    • [33] S. S. DRAGOMIR and G. H. TOADER, Some inequalities for m-convex functions, Studia Univ. Babe¸ s-Bolyai, Math., 38 (1), pp. 21-28,‏ (1993).‏
    • [34] A. M. FINK, A best possible Hadamard inequality, Math. Ineq. &‏ Appl., 2 , pp. 223-230, (1998).‏
    • [35] A. M. FINK, Toward a theory of best possible inequalities, Nieuw‏ Archief von Wiskunde, 12 , pp. 19-29, (1994).‏
    • [36] A. M. FINK, Two inequalities, Univ. Beograd Publ. Elektrotehn. Fak.‏ Ser. Mat., 6, pp. 48-49, (1995).‏
    • [37] B. GAVREA, On Hadamard’s inequality for the convex mappings defined on a convex domain in the space, Journal of Ineq. in Pure &‏...
    • [38] P. M. GILL, C. E. M. PEARCE and J. PECARIC, Hadamard’s inequality for r-convex functions, J. of Math. Anal. and Appl., 215 ,‏ pp. 461-470,...
    • [39] G. H. HARDY, J. E. LITTLEWOOD and G. POLYA, Inequalities, 2nd Ed., Cambridge University Press, (1952).‏
    • [40] K.-C. LEE and K.-L. TSENG, On a weighted generalisation of‏ Hadamard’s inequality for G-convex functions, Tamsui Oxford Journal‏ of Math....
    • [41] A. LUPAS, The Jensen-Hadamard inequality for convex functions of‏ higher order, Octogon Math. Mag., 5, No. 2, pp. 8-9, (1997).‏
    • [42] A. LUPAS, A generalisation of Hadamard’s inequality for convex functions, Univ. Beograd. Publ. Elek. Fak. Ser. Mat. Fiz., No. 544-576,...
    • [43] D. M. MAKISIMOVIC, A short proof of generalized Hadamard’s inequalities, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz., No.‏...
    • [44] D.S. MITRINOVIC and I. LACKOVIC, Hermite and convexity, Aequat. Math., 28, pp. 229—232, (1985).‏
    • [45] D. S. MITRINOVIC, J. E. PECARIC and A. M. FINK, Classical‏ and New Inequalities in Analysis, Kluwer Academic Publishers, Dordrecht/Boston/London.‏
    • [46] E. NEUMAN, Inequalities involving generalised symmetric means, J.‏ Math. Anal. Appl., 120, pp. 315-320, (1986).‏
    • [47] E. NEUMAN and J. E. PECARIC, Inequalities involving multivariate convex functions, J. Math. Anal. Appl., 137, pp. 514-549, (1989).‏
    • [48] E. NEUMAN, Inequalities involving multivariate convex functions II,‏ Proc. Amer. Math. Soc., 109, pp. 965-974, (1990).‏
    • [49] C. P. NICULESCU, A note on the dual Hermite-Hadamard inequality,‏ The Math. Gazette, July (2000).‏
    • [50] C. P. NICULESCU, Convexity according to the geometric mean, Math.‏ Ineq. & Appl., 3 (2), pp. 155-167, (2000).‏
    • [51] C. E. M. PEARCE, J. PECARIC and V. ´ SIMI ˇ C, Stolarsky means and Hadamard’s inequality, J. Math. Anal. Appl., 220, pp. 99-109, (1998).‏
    • [52] C. E. M. PEARCE and A. M. RUBINOV, P-functions, quasi-convex‏ functions and Hadamard-type inequalities, J. Math. Anal. Appl., 240, (1),...
    • [53] J. E. PECARIC, Remarks on two interpolations of Hadamard’s inequalities, Contributions, Macedonian Acad. of Sci. and Arts, Sect. of‏...
    • [54] J. PECARIC and S. S. DRAGOMIR, A generalization of Hadamard’s integral inequality for isotonic linear functionals, Rudovi Mat. (Sarajevo),...
    • [55] J. PECARIC, F. PROSCHAN and Y. L. TONG, Convex Functions,‏ Partial Orderings and Statistical Applications, Academic Press, Inc.,‏ (1992).‏
    • [56] J. SANDOR, A note on the Jensen-Hadamard inequality, Anal. Numer. Theor. Approx., 19, No. 1, pp. 29-34, (1990).‏
    • [57] J. SANDOR, An application of the Jensen-Hadamard inequality,‏ Nieuw-Arch.-Wisk., 8, No. 1, pp. 63-66, (1990).‏
    • [58] J. SANDOR, On the Jensen-Hadamard inequality, Studia Univ. BabesBolyai, Math., 36, No. 1, pp. 9-15, (1991).‏
    • [59] P. M. VASIC, I. B. LACKOVIC and D. M. MAKSIMOVIC, Note on convex functions IV: OnHadamard’s inequality for weighted arithmetic‏ means,...
    • [60] G. S. YANG and M. C. HONG, A note on Hadamard’s inequality,‏ Tamkang J. Math., 28 (1), pp. 33-37, (1997).‏
    • [61] G. S. YANG and K. L. TSENG, On certain integral inequalities related‏ to Hermite-Hadamard inequalities, J. Math. Anal. Appl., 239, pp.‏...
Fundación Dialnet

Mi Documat

Opciones de artículo

Opciones de compartir

Opciones de entorno