-
Previous Article
Jensen's inequality for quasiconvex functions
- NACO Home
- This Issue
-
Next Article
On Markovian solutions to Markov Chain BSDEs
Some new bounds for two mappings related to the Hermite-Hadamard inequality for convex functions
1. | Mathematics, School of Engineering & Science, Victoria University, PO Box 14428 Melbourne City, MC 8001, Australia, Australia |
References:
[1] |
A. G. Azpeitia, Convex functions and the Hadamard inequality, Rev. Colombiana Mat., 28 (1994), 7-12. |
[2] |
S. S. Dragomir, A mapping in connection to Hadamard's inequalities, An. Öster. Akad. Wiss. Math. Natur., (Wien), 128 (1991), 17-20. |
[3] |
S. S. Dragomir, Two mappings in connection to Hadamard's inequalities, J. Math. Anal. Appl., 167 (1992), 49-56.
doi: 10.1016/0022-247X(92)90233-4. |
[4] |
S. S. Dragomir, On Hadamard's inequalities for convex functions, Mat. Balkanica, 6 (1992), 215-222. |
[5] |
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), Art. 35. Available from: http://www.emis.de/journals/JIPAM/article187.html?sid=187 |
[6] |
S. S. Dragomir, Bounds for the normalized Jensen functional, Bull. Austral. Math. Soc., 74 (2006), 471-476.
doi: 10.1017/S000497270004051X. |
[7] |
S. S. Dragomir and I. Gomm, Bounds for two mappings associated to the Hermite-Hadamard inequality, Aust. J. Math. Anal. Appl., 8 (2011), 9 pages. |
[8] |
S. S. Dragomir, D. S. Milośević and J. Sándor, On some refinements of Hadamard's inequalities and applications, Univ. Belgrad, Publ. Elek. Fak. Sci. Math., 4 (1993), 21-24. |
[9] |
S. S. Dragomir and C. E. M. Pearce, "Selected Topics on Hermite-Hadamard Inequalities and Applications," RGMIA Monographs, 2000. Available from: http://rgmia.org/monographs/hermite_hadamard.html |
[10] |
A. Guessab and G. Schmeisser, Sharp integral inequalities of the Hermite-Hadamard type, J. Approx. Theory, 115 (2002), 260-288.
doi: 10.1006/jath.2001.3658. |
[11] |
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., 13 (2010), 1-32. |
[12] |
M. Merkle, Remarks on Ostrowski's and Hadamard's inequality, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat., 10 (1999), 113-117. |
[13] |
C. E. M. Pearce and A. M. Rubinov, P-functions, quasi-convex functions, and Hadamard type inequalities, J. Math. Anal. Appl., 240 (1999), 92-104.
doi: 10.1006/jmaa.1999.6593. |
[14] |
J. Pečarić and A. Vukelić, "Hadamard and Dragomir-Agarwal inequalities, the Euler formulae and convex functions," Functional Equations, Inequalities and Applications, Kluwer Acad. Publ., Dordrecht, (2003), 105-137. |
[15] |
G. Toader, Superadditivity and Hermite-Hadamard's inequalities, Studia Univ. Babeş-Bolyai Math., 39 (1994), 27-32. |
[16] |
G. S. Yang and M. C. Hong, A note on Hadamard's inequality, Tamkang J. Math., 28 (1997), 33-37. |
[17] |
G. S. Yang and K. L. Tseng, On certain integral inequalities related to Hermite-Hadamard inequalities, J. Math. Anal. Appl., 239 (1999), 180-187.
doi: 10.1006/jmaa.1999.6506. |
show all references
References:
[1] |
A. G. Azpeitia, Convex functions and the Hadamard inequality, Rev. Colombiana Mat., 28 (1994), 7-12. |
[2] |
S. S. Dragomir, A mapping in connection to Hadamard's inequalities, An. Öster. Akad. Wiss. Math. Natur., (Wien), 128 (1991), 17-20. |
[3] |
S. S. Dragomir, Two mappings in connection to Hadamard's inequalities, J. Math. Anal. Appl., 167 (1992), 49-56.
doi: 10.1016/0022-247X(92)90233-4. |
[4] |
S. S. Dragomir, On Hadamard's inequalities for convex functions, Mat. Balkanica, 6 (1992), 215-222. |
[5] |
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), Art. 35. Available from: http://www.emis.de/journals/JIPAM/article187.html?sid=187 |
[6] |
S. S. Dragomir, Bounds for the normalized Jensen functional, Bull. Austral. Math. Soc., 74 (2006), 471-476.
doi: 10.1017/S000497270004051X. |
[7] |
S. S. Dragomir and I. Gomm, Bounds for two mappings associated to the Hermite-Hadamard inequality, Aust. J. Math. Anal. Appl., 8 (2011), 9 pages. |
[8] |
S. S. Dragomir, D. S. Milośević and J. Sándor, On some refinements of Hadamard's inequalities and applications, Univ. Belgrad, Publ. Elek. Fak. Sci. Math., 4 (1993), 21-24. |
[9] |
S. S. Dragomir and C. E. M. Pearce, "Selected Topics on Hermite-Hadamard Inequalities and Applications," RGMIA Monographs, 2000. Available from: http://rgmia.org/monographs/hermite_hadamard.html |
[10] |
A. Guessab and G. Schmeisser, Sharp integral inequalities of the Hermite-Hadamard type, J. Approx. Theory, 115 (2002), 260-288.
doi: 10.1006/jath.2001.3658. |
[11] |
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., 13 (2010), 1-32. |
[12] |
M. Merkle, Remarks on Ostrowski's and Hadamard's inequality, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat., 10 (1999), 113-117. |
[13] |
C. E. M. Pearce and A. M. Rubinov, P-functions, quasi-convex functions, and Hadamard type inequalities, J. Math. Anal. Appl., 240 (1999), 92-104.
doi: 10.1006/jmaa.1999.6593. |
[14] |
J. Pečarić and A. Vukelić, "Hadamard and Dragomir-Agarwal inequalities, the Euler formulae and convex functions," Functional Equations, Inequalities and Applications, Kluwer Acad. Publ., Dordrecht, (2003), 105-137. |
[15] |
G. Toader, Superadditivity and Hermite-Hadamard's inequalities, Studia Univ. Babeş-Bolyai Math., 39 (1994), 27-32. |
[16] |
G. S. Yang and M. C. Hong, A note on Hadamard's inequality, Tamkang J. Math., 28 (1997), 33-37. |
[17] |
G. S. Yang and K. L. Tseng, On certain integral inequalities related to Hermite-Hadamard inequalities, J. Math. Anal. Appl., 239 (1999), 180-187.
doi: 10.1006/jmaa.1999.6506. |
[1] |
Tomasz Szostok. Inequalities of Hermite-Hadamard type for higher order convex functions, revisited. Communications on Pure and Applied Analysis, 2021, 20 (2) : 903-914. doi: 10.3934/cpaa.2020296 |
[2] |
Shu-Lin Lyu. On the Hermite--Hadamard inequality for convex functions of two variables. Numerical Algebra, Control and Optimization, 2014, 4 (1) : 1-8. doi: 10.3934/naco.2014.4.1 |
[3] |
Ruonan Liu, Run Xu. Hermite-Hadamard type inequalities for harmonical $ (h1,h2)- $convex interval-valued functions. Mathematical Foundations of Computing, 2021, 4 (2) : 89-103. doi: 10.3934/mfc.2021005 |
[4] |
Leon Ehrenpreis. Special functions. Inverse Problems and Imaging, 2010, 4 (4) : 639-647. doi: 10.3934/ipi.2010.4.639 |
[5] |
Liran Rotem. Banach limit in convexity and geometric means for convex bodies. Electronic Research Announcements, 2016, 23: 41-51. doi: 10.3934/era.2016.23.005 |
[6] |
Aleksandra Čižmešija, Iva Franjić, Josip Pečarić, Dora Pokaz. On a family of means generated by the Hardy-Littlewood maximal inequality. Numerical Algebra, Control and Optimization, 2012, 2 (2) : 223-231. doi: 10.3934/naco.2012.2.223 |
[7] |
S. S. Dragomir, C. E. M. Pearce. Jensen's inequality for quasiconvex functions. Numerical Algebra, Control and Optimization, 2012, 2 (2) : 279-291. doi: 10.3934/naco.2012.2.279 |
[8] |
Małgorzata Wyrwas, Dorota Mozyrska, Ewa Girejko. Subdifferentials of convex functions on time scales. Discrete and Continuous Dynamical Systems, 2011, 29 (2) : 671-691. doi: 10.3934/dcds.2011.29.671 |
[9] |
Leandro M. Del Pezzo, Nicolás Frevenza, Julio D. Rossi. Convex and quasiconvex functions in metric graphs. Networks and Heterogeneous Media, 2021, 16 (4) : 591-607. doi: 10.3934/nhm.2021019 |
[10] |
Jacques Wolfmann. Special bent and near-bent functions. Advances in Mathematics of Communications, 2014, 8 (1) : 21-33. doi: 10.3934/amc.2014.8.21 |
[11] |
Gang Li, Lipu Zhang, Zhe Liu. The stable duality of DC programs for composite convex functions. Journal of Industrial and Management Optimization, 2017, 13 (1) : 63-79. doi: 10.3934/jimo.2016004 |
[12] |
Zhongliang Deng, Enwen Hu. Error minimization with global optimization for difference of convex functions. Discrete and Continuous Dynamical Systems - S, 2019, 12 (4&5) : 1027-1033. doi: 10.3934/dcdss.2019070 |
[13] |
Khalida Inayat Noor, Muhammad Aslam Noor. Higher order uniformly close-to-convex functions. Discrete and Continuous Dynamical Systems - S, 2015, 8 (6) : 1277-1290. doi: 10.3934/dcdss.2015.8.1277 |
[14] |
Luigi Ambrosio, Camillo Brena. Stability of a class of action functionals depending on convex functions. Discrete and Continuous Dynamical Systems, 2022 doi: 10.3934/dcds.2022055 |
[15] |
Davide La Torre, Simone Marsiglio, Franklin Mendivil, Fabio Privileggi. Public debt dynamics under ambiguity by means of iterated function systems on density functions. Discrete and Continuous Dynamical Systems - B, 2021, 26 (11) : 5873-5903. doi: 10.3934/dcdsb.2021070 |
[16] |
Chihiro Matsuoka, Koichi Hiraide. Special functions created by Borel-Laplace transform of Hénon map. Electronic Research Announcements, 2011, 18: 1-11. doi: 10.3934/era.2011.18.1 |
[17] |
Krzysztof Frączek, M. Lemańczyk, E. Lesigne. Mild mixing property for special flows under piecewise constant functions. Discrete and Continuous Dynamical Systems, 2007, 19 (4) : 691-710. doi: 10.3934/dcds.2007.19.691 |
[18] |
Gümrah Uysal. On a special class of modified integral operators preserving some exponential functions. Mathematical Foundations of Computing, 2022 doi: 10.3934/mfc.2021044 |
[19] |
Masao Fukushima. A class of gap functions for quasi-variational inequality problems. Journal of Industrial and Management Optimization, 2007, 3 (2) : 165-171. doi: 10.3934/jimo.2007.3.165 |
[20] |
Van Hoang Nguyen. The Hardy–Moser–Trudinger inequality via the transplantation of Green functions. Communications on Pure and Applied Analysis, 2020, 19 (7) : 3559-3574. doi: 10.3934/cpaa.2020155 |
Impact Factor:
Tools
Metrics
Other articles
by authors
[Back to Top]