| Title:
|
A sequence of mappings associated with the Hermite-Hadamard inequalities and applications (English) |
| Author:
|
Dragomir, Sever S. |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
49 |
| Issue:
|
2 |
| Year:
|
2004 |
| Pages:
|
123-140 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
New properties for some sequences of functions defined by multiple integrals associated with the Hermite-Hadamard integral inequality for convex functions and some applications are given. (English) |
| Keyword:
|
Hermite-Hadamard inequality |
| MSC:
|
26D10 |
| MSC:
|
26D15 |
| MSC:
|
26D99 |
| idZBL:
|
Zbl 1099.26016 |
| idMR:
|
MR2043078 |
| DOI:
|
10.1023/B:APOM.0000027220.51557.6d |
| . |
| Date available:
|
2009-09-22T18:17:18Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134563 |
| . |
| Reference:
|
[1] G. Allasia, C. Giordano, J. Pečarić: Hadamard-type inequalities for $(2r)$-convex functions with applications.Atti Accad. Sci. Torino Cl. Sci. Fis. Mat. Natur. 133 (1999), 187–200. MR 1799453 |
| Reference:
|
[2] H. Alzer: A note on Hadamard’s inequalities.C. R. Math. Rep. Acad. Sci. Canada 11 (1989), 255–258. Zbl 0707.26012, MR 1030364 |
| Reference:
|
[3] H. Alzer: On an integral inequality.Anal. Numér. Théor. Approx. 18 (1989), 101–103. Zbl 0721.26011, MR 1089226 |
| Reference:
|
[4] A. G. Azpeitia: Convex functions and the Hadamard inequality.Rev. Colombiana Mat. 28 (1994), 7–12. Zbl 0832.26015, MR 1304041 |
| Reference:
|
[5] D. Barbu, S. S. Dragomir and C. Buşe: A probabilistic argument for the convergence of some sequences associated to Hadamard’s inequality.Studia Univ. Babeş-Bolyai Math. 38 (1993), 29–33. MR 1863680 |
| Reference:
|
[6] C. Buşe, S. S. Dragomir and D. Barbu: The convergence of some sequences connected to Hadamard’s inequality.Demostratio Math. 29 (1996), 53–59. MR 1398727, 10.1515/dema-1996-0109 |
| Reference:
|
[7] S. S. Dragomir: A mapping in connection to Hadamard’s inequalities.Anz. Österreich. Akad. Wiss. Math.-Natur. Kl. 128 (1991), 17–20. Zbl 0747.26015, MR 1188722 |
| Reference:
|
[8] S. S. Dragomir: A refinement of Hadamard’s inequality for isotonic linear functionals.Tamkang J. Math. 24 (1993), 101–106. Zbl 0799.26016, MR 1215250 |
| Reference:
|
[9] S. S. Dragomir: On Hadamard’s inequalities for convex functions.Mat. Balkanica (N. S.) 6 (1992), 215–222. Zbl 0834.26010, MR 1183627 |
| Reference:
|
[10] S. S. Dragomir: On Hadamard’s inequality for the convex mappings defined on a ball in the space and applications.Math. Inequal. Appl. 3 (2000), 177–187. Zbl 0951.26010, MR 1749295 |
| Reference:
|
[11] S. S. Dragomir: On Hadamard’s inequality on a disk.JIPAM. J. Inequal. Pure Appl. Math. 1 (2000), http://jipam.vu.edu.au/, Electronic. Zbl 0948.26012, MR 1756653 |
| Reference:
|
[12] S. S. Dragomir: Some integral inequalities for differentiable convex functions.Makedon. Akad. Nauk Umet. Oddel. Mat.-Tehn. Nauk. Prilozi 13 (1992), 13–17. Zbl 0770.26009, MR 1262519 |
| Reference:
|
[13] S. S. Dragomir: Some remarks on Hadamard’s inequalities for convex functions.Extracta Math. 9 (1994), 88–94. Zbl 0984.26012, MR 1325288 |
| Reference:
|
[14] S. S. Dragomir: Two mappings in connection to Hadamard’s inequalities.J. Math. Anal. Appl. 167 (1992), 49–56. Zbl 0758.26014, MR 1165255, 10.1016/0022-247X(92)90233-4 |
| Reference:
|
[15] S. S. Dragomir, R. P. Agarwal: Two new mappings associated with Hadamard’s inequalities for convex functions.Appl. Math. Lett. 11 (1998), 33–38. MR 1628995, 10.1016/S0893-9659(98)00030-5 |
| Reference:
|
[16] S. S. Dragomir, C. Buşe: Refinements of Hadamard’s inequality for multiple integrals.Utilitas Math. 47 (1995), 193–198. MR 1330902 |
| Reference:
|
[17] 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 (2000), 489–501. MR 1758551, 10.1006/jmaa.2000.6769 |
| Reference:
|
[18] S. S. Dragomir, S. Fitzpatrick: Hadamard inequality for $s$-convex functions in the first sense and applications.Demonstratio Math. 31 (1998), 633–642. MR 1658478 |
| Reference:
|
[19] S. S. Dragomir, S. Fitzpatrick: The Hadamard’s inequality for $s$-convex functions in the second sense.Demonstratio Math. 32 (1999), 687–696. MR 1740330 |
| Reference:
|
[20] S. S. Dragomir, N. M. Ionescu: On some inequalities for convex-dominated functions.Anal. Numér. Théor. Approx. 19 (1990), 21–27. MR 1159773 |
| Reference:
|
[21] S. S. Dragomir, D. S. Milośević and J. Sándor: On some refinements of Hadamard’s inequalities and applications.Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. 4 (1993), 3–10. |
| Reference:
|
[22] S. S. Dragomir, B. Mond: On Hadamard’s inequality for a class of functions of Godunova and Levin.Indian J. Math. 39 (1997), 1–9. MR 1476079 |
| Reference:
|
[23] S. S. Dragomir, C. E. M. Pearce: Quasi-convex functions and Hadamard’s inequality.Bull. Austral. Math. Soc. 57 (1998), 377–385. MR 1623227, 10.1017/S0004972700031786 |
| Reference:
|
[24] S. S. Dragomir, C. E. M. Pearce, and J. E. Pečarić: On Jessen’s related inequalities for isotonic sublinear functionals.Acta Sci. Math. 61 (1995), 373–382. MR 1377372 |
| Reference:
|
[25] S. S. Dragomir, J. E. Pečarić, and L. E. Persson: Some inequalities of Hadamard type.Soochow J. Math. 21 (1995), 335–341. MR 1348130 |
| Reference:
|
[26] S. S. Dragomir, J. E. Pečarić, and J. Sándor: A note on the Jensen-Hadamard inequality.Anal. Numér. Théor. Approx. 19 (1990), 29–34. MR 1159774 |
| Reference:
|
[27] S. S. Dragomir, G. H. Toader: Some inequalities for $m$-convex functions.Studia Univ. Babeş-Bolyai Math. 38 (1993), 21–28. MR 1863679 |
| Reference:
|
[28] A. M. Fink: A best possible Hadamard inequality.Math. Inequal. Appl. 1 (1998), 223–230. Zbl 0907.26009, MR 1613456 |
| Reference:
|
[29] A. M. Fink: Toward a theory of best possible inequalities.Nieuw Arch. Wisk. 12 (1994), 19–29. Zbl 0827.26018, MR 1284677 |
| Reference:
|
[30] A. M. Fink: Two inequalities.Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. 6 (1995), 48–49. Zbl 0841.26009, MR 1367482 |
| Reference:
|
[31] B. Gavrea: On Hadamard’s inequality for the convex mappings defined on a convex domain in the space.JIPAM. J. Inequal. Pure Appl. Math. 1 (2000), Article 9, http://jipam.vu.edu.au/, Electronic. Zbl 0949.26008, MR 1756660 |
| Reference:
|
[32] P. M. Gill, C. E. M. Pearce and J. Pečarić: Hadamard’s inequality for $r$-convex functions.J. Math. Anal. Appl. 215 (1997), 461–470. MR 1490762, 10.1006/jmaa.1997.5645 |
| Reference:
|
[33] G. H. Hardy, J. E. Littlewood, and G. Pólya: Inequalities. 2nd ed.Cambridge University Press, 1952. MR 0046395 |
| Reference:
|
[34] K.-C. Lee, K.-L. Tseng: On weighted generalization of Hadamard’s inequality for $g$ functions.Tamsui Oxf. J. Math. Sci. 16 (2000), 91–104. MR 1772077 |
| Reference:
|
[35] A. Lupaş: The Jensen-Hadamard inequality for convex functions of higher order.Octogon Math. Mag. 5 (1997), 8–9. MR 1619472 |
| Reference:
|
[36] A. Lupaş: A generalization of Hadamard’s inequality for convex functions.Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz. 544–576 (1976), 115–121. MR 0444865 |
| Reference:
|
[37] D. M. Maksimović: A short proof of generalized Hadamard’s inequalities.Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz. 634–677 (1979), 126–128. MR 0579274 |
| Reference:
|
[38] D. S. Mitrinović, I. Lacković: Hermite and convexity.Aequationes Math. 28 (1985), 229–232. MR 0791622, 10.1007/BF02189414 |
| Reference:
|
[39] D. S. Mitrinović, J. E. Pečarić, and A. M. Fink: Classical and New Inequalities in Analysis.Kluwer Academic Publishers, Dordrecht, 1993. MR 1220224 |
| Reference:
|
[40] E. Neuman: Inequalities involving generalized symmetric means.J. Math. Anal. Appl. 120 (1986), 315–320. Zbl 0601.26013, MR 0861922, 10.1016/0022-247X(86)90218-0 |
| Reference:
|
[41] E. Neuman, J. E. Pečarić: Inequalities involving multivariate convex functions.J. Math. Anal. Appl. 137 (1989), 514–549. MR 0984976, 10.1016/0022-247X(89)90262-X |
| Reference:
|
[42] E. Neuman: Inequalities involving multivariate convex functions. II.Proc. Amer. Math. Soc. 109 (1990), 965–974. Zbl 0699.26009, MR 1009996 |
| Reference:
|
[43] C. P. Niculescu: A note on the dual Hermite-Hadamard inequality.The Math. Gazette (July 2000), . |
| Reference:
|
[44] C. P. Niculescu: Convexity according to the geometric mean.Math. Inequal. Appl. 3 (2000), 155–167. Zbl 0952.26006, MR 1749293 |
| Reference:
|
[45] C. E. M. Pearce, J. Pečarić, and V. Šimić: Stolarsky means and Hadamard’s inequality.J. Math. Anal. Appl. 220 (1998), 99–109. MR 1612079, 10.1006/jmaa.1997.5822 |
| Reference:
|
[46] C. E. M. Pearce, A. M. Rubinov: $P$-functions, quasi-convex functions and Hadamard-type inequalities.J. Math. Anal. Appl. 240 (1999), 92–104. MR 1728202, 10.1006/jmaa.1999.6593 |
| Reference:
|
[47] J. E. Pečarić: Remarks on two interpolations of Hadamard’s inequalities.Makedon. Akad. Nauk. Umet. Oddel. Mat.-Tehn. Nauk. Prilozi 13 (1992), 9–12. MR 1262518 |
| Reference:
|
[48] J. Pečarić, S. S. Dragomir: A generalization of Hadamard’s inequality for isotonic linear functionals.Rad. Mat. 7 (1991), 103–107. MR 1126888 |
| Reference:
|
[49] J. Pečarić, F. Proschan, and Y. L. Tong: Convex Functions, Partial Orderings and Statistical Applications.Academic Press, Boston, 1992. MR 1162312 |
| Reference:
|
[50] J. Sándor: An application of the Jensen-Hadamard inequality.Nieuw Arch. Wisk. 8 (1990), 63–66. MR 1056662 |
| Reference:
|
[51] J. Sándor: On the Jensen-Hadamard inequality.Studia Univ. Babeş-Bolyai, Math. 36 (1991), 9–15. MR 1280888 |
| Reference:
|
[52] P. M. Vasić, I. B. Lacković, and D. M. Maksimović: Note on convex functions. IV. On Hadamard’s inequality for weighted arithmetic means.Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz. 678–715 (1980), 199–205. |
| Reference:
|
[53] G. S Yang, M. C. Hong: A note on Hadamard’s inequality.Tamkang J. Math. 28 (1997), 33–37. MR 1457248 |
| Reference:
|
[54] G. S. Yang, K. L. Tseng: On certain integral inequalities related to Hermite-Hadamard inequalities.J. Math. Anal. Appl. 239 (1999), 180–187. MR 1719056, 10.1006/jmaa.1999.6506 |
| . |
