On same refinements of companions Fejér's
DOI:
https://doi.org/10.4067/S0716-09172012000400001Keywords:
Hermite-Hadamard Inequality, convex function, Fejer inequality, superquadratic function, desigualdad de Hermite-Hadamard, función convexa, desigualdad de Fejer, función supercuadrática.Abstract
In this paper some companions of Fejer’s inequality for superquadratic functions are given, we also get refinements of some known results proved in [18].
References
[1] S. Abramovich, S. Banic, M. Matic, J. Pecaric, Jensen—Steffensen’s and related inequalities for superquadratic functions, Math. Ineq. Appl., 11, pp. 23—41, (2008).
[2] S. Abramovich, J. Baric, J. Pecaric, Fejer and Hermite-Hadamard type inequalities for superquadratic functions, Math. J. Anal. Appl., 344, pp. 1048-1056, (2008).
[3] S. Abramovich, G. Jameson, G. Sinnamon, Refining Jensen’s inequality, Bull. Math. Soc. Sci. Math. Roumanie (N.S.) 47 (95), pp. 3—14, (2004).
[4] S. Banic, J. Pecaric, S. Varosanec, Superquadratic functions and refinements of some classical inequalities, J. Korean Math. Soc. 45, pp. 513—525, (2008).
[5] S. Banic, Superquadratic functions, PhD thesis, Zagreb (in Croatian), (2007).
[6] S. S. Dragomir, Two mappings in connection to Hadamard’s inequalities, J. Math. Anal. Appl., 167, pp. 49—56, (1992).
[7] S. S. Dragomir, Further properties of some mappings associated with Hermite-Hadamard inequalities, Tamkang. J. Math., 34 (1), pp. 45—57, (2003).
[8] S. S. Dragomir, Y.J. Cho and S.S. Kim, Inequalities of Hadamard’s type for Lipschitzian mappings and their applications, J. Math. Anal. Appl., 245, pp. 489—501, (2000).
[9] S. S. Dragomir, D.S. Milosevic and J. Sandor, On some refinements of Hadamard’s inequalities and applications, Univ. Belgrad. Publ. Elek. Fak. Sci. Math., 4, pp. 3—10, (1993).
[10] L. Fejer, Uber die Fourierreihen, II, Math. Naturwiss. Anz Ungar. Akad. Wiss., 24, pp. 369—390, (1906). (In Hungarian).
[11] Ming-In Ho, Fejer inequalities for Wright-convex functions, JIPAM. J. Inequal. Pure Appl. Math. 8 (1), (2007), article 9.
[12] J. Hadamard, Etude sur les proprietes des fonctions entieres en particulier d’une function consideree par Riemann J. Math. Pures and Appl., 58, pp. 171-215, (1983).
[13] M. A. Latif, On some refinements of Fejer type inequalities via superquadratic functions.(to appear).
[14] M. A. Latif, On some new Fejer-type inequalities for superquadratic functions. (to appear).
[15] K. L. Tseng, S. R. Hwang and S.S. Dragomir, On some new inequalities of Hermite-Hadamard- Fejer type involving convex functions, Demonstratio Math., XL (1), pp. 51—64, (2007).
[16] K. L. Tseng, S. R. Hwang and S.S. Dragomir, Fejer-type Inequalities (I), (Submitted) Preprint RGMIA Res. Rep. Coll. 12 (2009), No.4, Article 5. [Online http://www.staff.vu.edu.au/RGMIA/v12n4.asp.].
[17] K. L. Tseng, S.R. Hwang and S.S. Dragomir, Fejer-type Inequalities (II), (Submitted) Preprint RGMIA Res. Rep. Coll. 12 (2009), Supplement, Article 16, pp.1-12. [Online http://www.staff.vu.edu.au/RGMIA/v12(E).asp.].
[18] K. L. Tseng, S. R. Hwang and S.S. Dragomir, Some companions of Fejer’s inequality for convex functions, (Submitted) Preprint RGMIA Res. Rep. Coll. 12 (2009), Supplement, Article 19, pp.1-12. [Online http://www.staff.vu.edu.au/RGMIA/v12(E).asp.].
[19] G.S. Yang and K.L. Tseng, Inequalities of Hermite-Hadamard-Fejer type for convex functions and Lipschitzian functions, Taiwanese J. Math., 7(3), pp. 433—440, (2003).
[2] S. Abramovich, J. Baric, J. Pecaric, Fejer and Hermite-Hadamard type inequalities for superquadratic functions, Math. J. Anal. Appl., 344, pp. 1048-1056, (2008).
[3] S. Abramovich, G. Jameson, G. Sinnamon, Refining Jensen’s inequality, Bull. Math. Soc. Sci. Math. Roumanie (N.S.) 47 (95), pp. 3—14, (2004).
[4] S. Banic, J. Pecaric, S. Varosanec, Superquadratic functions and refinements of some classical inequalities, J. Korean Math. Soc. 45, pp. 513—525, (2008).
[5] S. Banic, Superquadratic functions, PhD thesis, Zagreb (in Croatian), (2007).
[6] S. S. Dragomir, Two mappings in connection to Hadamard’s inequalities, J. Math. Anal. Appl., 167, pp. 49—56, (1992).
[7] S. S. Dragomir, Further properties of some mappings associated with Hermite-Hadamard inequalities, Tamkang. J. Math., 34 (1), pp. 45—57, (2003).
[8] S. S. Dragomir, Y.J. Cho and S.S. Kim, Inequalities of Hadamard’s type for Lipschitzian mappings and their applications, J. Math. Anal. Appl., 245, pp. 489—501, (2000).
[9] S. S. Dragomir, D.S. Milosevic and J. Sandor, On some refinements of Hadamard’s inequalities and applications, Univ. Belgrad. Publ. Elek. Fak. Sci. Math., 4, pp. 3—10, (1993).
[10] L. Fejer, Uber die Fourierreihen, II, Math. Naturwiss. Anz Ungar. Akad. Wiss., 24, pp. 369—390, (1906). (In Hungarian).
[11] Ming-In Ho, Fejer inequalities for Wright-convex functions, JIPAM. J. Inequal. Pure Appl. Math. 8 (1), (2007), article 9.
[12] J. Hadamard, Etude sur les proprietes des fonctions entieres en particulier d’une function consideree par Riemann J. Math. Pures and Appl., 58, pp. 171-215, (1983).
[13] M. A. Latif, On some refinements of Fejer type inequalities via superquadratic functions.(to appear).
[14] M. A. Latif, On some new Fejer-type inequalities for superquadratic functions. (to appear).
[15] K. L. Tseng, S. R. Hwang and S.S. Dragomir, On some new inequalities of Hermite-Hadamard- Fejer type involving convex functions, Demonstratio Math., XL (1), pp. 51—64, (2007).
[16] K. L. Tseng, S. R. Hwang and S.S. Dragomir, Fejer-type Inequalities (I), (Submitted) Preprint RGMIA Res. Rep. Coll. 12 (2009), No.4, Article 5. [Online http://www.staff.vu.edu.au/RGMIA/v12n4.asp.].
[17] K. L. Tseng, S.R. Hwang and S.S. Dragomir, Fejer-type Inequalities (II), (Submitted) Preprint RGMIA Res. Rep. Coll. 12 (2009), Supplement, Article 16, pp.1-12. [Online http://www.staff.vu.edu.au/RGMIA/v12(E).asp.].
[18] K. L. Tseng, S. R. Hwang and S.S. Dragomir, Some companions of Fejer’s inequality for convex functions, (Submitted) Preprint RGMIA Res. Rep. Coll. 12 (2009), Supplement, Article 19, pp.1-12. [Online http://www.staff.vu.edu.au/RGMIA/v12(E).asp.].
[19] G.S. Yang and K.L. Tseng, Inequalities of Hermite-Hadamard-Fejer type for convex functions and Lipschitzian functions, Taiwanese J. Math., 7(3), pp. 433—440, (2003).
Published
2013-02-19
How to Cite
[1]
M. A. Latif, “On same refinements of companions Fejér’s”, Proyecciones (Antofagasta, On line), vol. 31, no. 4, pp. 309-332, Feb. 2013.
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