-
Previous Article
How to transform matrices $U_1, \ldots, U_p$ to matrices $V_1, \ldots, V_p$ so that $V_i V_j^T= {\mathbb O} $ if $ i \neq j $?
- NACO Home
- This Issue
-
Next Article
Some new bounds for two mappings related to the Hermite-Hadamard inequality for convex functions
Jensen's inequality for quasiconvex functions
1. | Mathematics, School of Engineering & Science, Victoria University, Melbourne, Australia |
2. | School of Mathematical Sciences, The University of Adelaide, Adelaide, Australia |
References:
[1] |
M. Alomari, M. Darus and S. S. Dragomir, New inequalities of Hermite-Hadamard type for functions whose second derivatives absolute values are quasi-convex, Tamkang J. Math, 41 (2010), 353-359. |
[2] |
M. Alomari, M. Darus and U. S. Kirmaci, Refinements of Hadamard-type inequalities for quasi-convex functions with applications to trapezoidal formula and to special means, Comput. Math. Appl., 59 (2010), 225-232.
doi: 10.1016/j.camwa.2009.08.002. |
[3] |
S. S. Dragomir, Two mappings associated with Jensen's inequality, Extracta Math., 8 (1993), 102-105. |
[4] |
S. S. Dragomir and D. M. Milošević, Two mappings in connection to Jensen's inequality, Zb. Rad. (Krajujevac), 15 (1994), 65-73. |
[5] |
S. S. Dragomir and D. M. Milošević, Two mappings in connection to Jensen's inequality, Math. Balkanica (N.S.), 9 (1995), 3-9. |
[6] |
S. S. Dragomir and B. Mond, On Hadamard's inequality for a class of functions of Godunova and Levin, Indian J. Math., 39 (1997), 1-9. |
[7] |
S. S. Dragomir and C. E. M. Pearce, On Jensen's inequality for a class of functions of Godunova and Levin, Periodica Math. Hungar., 33 (1996), 93-100.
doi: 10.1007/BF02093506. |
[8] |
S. S. Dragomir and C. E. M. Pearce, Quasi-convex functions and Hadamard's inequality, Bull. Austral. Math. Soc., 57 (1998), 377-385.
doi: 10.1017/S0004972700031786. |
[9] |
S. S. Dragomir, J. E. Pečarić and L. E. Persson, Some inequalities of Hadamard type, Soochow J. Math., 21 (1995), 335-341. |
[10] |
A. Eberhard and C. E. M. Pearce, Class-inclusion properties for convex functions, in "Progress in Optimization" (Perth 1998), Appl. Optim., Kluwer Acad. Publ., Dordrecht, 39 (2000), 129-133. |
[11] |
N. Hadjisavvas, Hadamard-type inequalities for quasiconvex functions, J. Inequal. Pure Appl. Math., 4 (2003), 6 pp. (electronic). |
[12] |
D. A. Ion, Some estimates on the Hermite-Hadamard inequality through quasi-convex functions, An. Univ. Craiova Ser. Mat. Inform., 34 (2007), 83-88. |
[13] |
M. Jovanović, Some inequalities for strong quasiconvex functions, Glas. Mat. Ser. III, 24 (1989), 25-29. |
[14] |
M. Merkle, Jensen's inequality for multivariate medians, J. Math. Anal. Appl., 370 (2010), 258-269.
doi: 10.1016/j.jmaa.2010.04.033. |
[15] |
C. E. M. Pearce, Quasiconvexity, fractional programming and extremal traffic congestion, in "Frontiers in Global Optimization," Kluwer, Dordrecht, "Nonlinear Optimization and its Applications", 74 (2004), 403-409. |
[16] |
C. E. M. Pearce and A. M. Rubinov, $P$-functions, quasi-convex functions and Hadamard-type inequalities, J. Math. Anal. Applic., 240 (1999), 92-104.
doi: 10.1006/jmaa.1999.6593. |
[17] |
A. M. Rubinov and J. Dutta, Hadamard type inequality for quasiconvex functions in higher dimensions, J. Math. Anal. Appl., 270 (2002), 80-91.
doi: 10.1016/S0022-247X(02)00050-1. |
[18] |
M. Wagner, Jensen's inequality for the lower semicontinuous quasiconvex envelope and relaxation of multidimensional control problems, J. Math. Anal. Appl., 355 (2009), 606-619.
doi: 10.1016/j.jmaa.2009.01.059. |
show all references
References:
[1] |
M. Alomari, M. Darus and S. S. Dragomir, New inequalities of Hermite-Hadamard type for functions whose second derivatives absolute values are quasi-convex, Tamkang J. Math, 41 (2010), 353-359. |
[2] |
M. Alomari, M. Darus and U. S. Kirmaci, Refinements of Hadamard-type inequalities for quasi-convex functions with applications to trapezoidal formula and to special means, Comput. Math. Appl., 59 (2010), 225-232.
doi: 10.1016/j.camwa.2009.08.002. |
[3] |
S. S. Dragomir, Two mappings associated with Jensen's inequality, Extracta Math., 8 (1993), 102-105. |
[4] |
S. S. Dragomir and D. M. Milošević, Two mappings in connection to Jensen's inequality, Zb. Rad. (Krajujevac), 15 (1994), 65-73. |
[5] |
S. S. Dragomir and D. M. Milošević, Two mappings in connection to Jensen's inequality, Math. Balkanica (N.S.), 9 (1995), 3-9. |
[6] |
S. S. Dragomir and B. Mond, On Hadamard's inequality for a class of functions of Godunova and Levin, Indian J. Math., 39 (1997), 1-9. |
[7] |
S. S. Dragomir and C. E. M. Pearce, On Jensen's inequality for a class of functions of Godunova and Levin, Periodica Math. Hungar., 33 (1996), 93-100.
doi: 10.1007/BF02093506. |
[8] |
S. S. Dragomir and C. E. M. Pearce, Quasi-convex functions and Hadamard's inequality, Bull. Austral. Math. Soc., 57 (1998), 377-385.
doi: 10.1017/S0004972700031786. |
[9] |
S. S. Dragomir, J. E. Pečarić and L. E. Persson, Some inequalities of Hadamard type, Soochow J. Math., 21 (1995), 335-341. |
[10] |
A. Eberhard and C. E. M. Pearce, Class-inclusion properties for convex functions, in "Progress in Optimization" (Perth 1998), Appl. Optim., Kluwer Acad. Publ., Dordrecht, 39 (2000), 129-133. |
[11] |
N. Hadjisavvas, Hadamard-type inequalities for quasiconvex functions, J. Inequal. Pure Appl. Math., 4 (2003), 6 pp. (electronic). |
[12] |
D. A. Ion, Some estimates on the Hermite-Hadamard inequality through quasi-convex functions, An. Univ. Craiova Ser. Mat. Inform., 34 (2007), 83-88. |
[13] |
M. Jovanović, Some inequalities for strong quasiconvex functions, Glas. Mat. Ser. III, 24 (1989), 25-29. |
[14] |
M. Merkle, Jensen's inequality for multivariate medians, J. Math. Anal. Appl., 370 (2010), 258-269.
doi: 10.1016/j.jmaa.2010.04.033. |
[15] |
C. E. M. Pearce, Quasiconvexity, fractional programming and extremal traffic congestion, in "Frontiers in Global Optimization," Kluwer, Dordrecht, "Nonlinear Optimization and its Applications", 74 (2004), 403-409. |
[16] |
C. E. M. Pearce and A. M. Rubinov, $P$-functions, quasi-convex functions and Hadamard-type inequalities, J. Math. Anal. Applic., 240 (1999), 92-104.
doi: 10.1006/jmaa.1999.6593. |
[17] |
A. M. Rubinov and J. Dutta, Hadamard type inequality for quasiconvex functions in higher dimensions, J. Math. Anal. Appl., 270 (2002), 80-91.
doi: 10.1016/S0022-247X(02)00050-1. |
[18] |
M. Wagner, Jensen's inequality for the lower semicontinuous quasiconvex envelope and relaxation of multidimensional control problems, J. Math. Anal. Appl., 355 (2009), 606-619.
doi: 10.1016/j.jmaa.2009.01.059. |
[1] |
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 |
[2] |
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 |
[3] |
Anat Amir. Sharpness of Zapolsky's inequality for quasi-states and Poisson brackets. Electronic Research Announcements, 2011, 18: 61-68. doi: 10.3934/era.2011.18.61 |
[4] |
Kewei Zhang. On non-negative quasiconvex functions with quasimonotone gradients and prescribed zero sets. Discrete and Continuous Dynamical Systems, 2008, 21 (1) : 353-366. doi: 10.3934/dcds.2008.21.353 |
[5] |
Felipe Riquelme. Ruelle's inequality in negative curvature. Discrete and Continuous Dynamical Systems, 2018, 38 (6) : 2809-2825. doi: 10.3934/dcds.2018119 |
[6] |
Emmanuel N. Barron, Rafal Goebel, Robert R. Jensen. The quasiconvex envelope through first-order partial differential equations which characterize quasiconvexity of nonsmooth functions. Discrete and Continuous Dynamical Systems - B, 2012, 17 (6) : 1693-1706. doi: 10.3934/dcdsb.2012.17.1693 |
[7] |
Pablo Raúl Stinga, Chao Zhang. Harnack's inequality for fractional nonlocal equations. Discrete and Continuous Dynamical Systems, 2013, 33 (7) : 3153-3170. doi: 10.3934/dcds.2013.33.3153 |
[8] |
Lena Noethen, Sebastian Walcher. Tikhonov's theorem and quasi-steady state. Discrete and Continuous Dynamical Systems - B, 2011, 16 (3) : 945-961. doi: 10.3934/dcdsb.2011.16.945 |
[9] |
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 |
[10] |
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 |
[11] |
Changliang Zhou, Chunqin Zhou. Extremal functions of Moser-Trudinger inequality involving Finsler-Laplacian. Communications on Pure and Applied Analysis, 2018, 17 (6) : 2309-2328. doi: 10.3934/cpaa.2018110 |
[12] |
Ahmet Sahiner, Gulden Kapusuz, Nurullah Yilmaz. A new smoothing approach to exact penalty functions for inequality constrained optimization problems. Numerical Algebra, Control and Optimization, 2016, 6 (2) : 161-173. doi: 10.3934/naco.2016006 |
[13] |
Frank Jochmann. A variational inequality in Bean's model for superconductors with displacement current. Discrete and Continuous Dynamical Systems, 2009, 25 (2) : 545-565. doi: 10.3934/dcds.2009.25.545 |
[14] |
Pierdomenico Pepe. A nonlinear version of Halanay's inequality for the uniform convergence to the origin. Mathematical Control and Related Fields, 2021 doi: 10.3934/mcrf.2021045 |
[15] |
Guodong Ma, Jinbao Jian. A QP-free algorithm of quasi-strongly sub-feasible directions for inequality constrained optimization. Journal of Industrial and Management Optimization, 2015, 11 (1) : 307-328. doi: 10.3934/jimo.2015.11.307 |
[16] |
Takeshi Fukao, Nobuyuki Kenmochi. Quasi-variational inequality approach to heat convection problems with temperature dependent velocity constraint. Discrete and Continuous Dynamical Systems, 2015, 35 (6) : 2523-2538. doi: 10.3934/dcds.2015.35.2523 |
[17] |
Bernard Dacorogna, Giovanni Pisante, Ana Margarida Ribeiro. On non quasiconvex problems of the calculus of variations. Discrete and Continuous Dynamical Systems, 2005, 13 (4) : 961-983. doi: 10.3934/dcds.2005.13.961 |
[18] |
Tomasz Cieślak. Trudinger-Moser type inequality for radially symmetric functions in a ring and applications to Keller-Segel in a ring. Discrete and Continuous Dynamical Systems - B, 2013, 18 (10) : 2505-2512. doi: 10.3934/dcdsb.2013.18.2505 |
[19] |
Jingbo Dou, Ye Li. Classification of extremal functions to logarithmic Hardy-Littlewood-Sobolev inequality on the upper half space. Discrete and Continuous Dynamical Systems, 2018, 38 (8) : 3939-3953. doi: 10.3934/dcds.2018171 |
[20] |
S. S. Dragomir, I. Gomm. Some new bounds for two mappings related to the Hermite-Hadamard inequality for convex functions. Numerical Algebra, Control and Optimization, 2012, 2 (2) : 271-278. doi: 10.3934/naco.2012.2.271 |
Impact Factor:
Tools
Metrics
Other articles
by authors
[Back to Top]