Jensen's inequality for quasiconvex functions
Pages: 279  291,
Issue 2,
June
2012
doi:10.3934/naco.2012.2.279 Abstract
References
Full text (179.1K)
Related Articles
S. S. Dragomir  Mathematics, School of Engineering & Science, Victoria University, Melbourne, Australia (email)
C. E. M. Pearce  School of Mathematical Sciences, The University of Adelaide, Adelaide, Australia (email)
1 
M. Alomari, M. Darus and S. S. Dragomir, New inequalities of HermiteHadamard type for functions whose second derivatives absolute values are quasiconvex, Tamkang J. Math, 41 (2010), 353359. 

2 
M. Alomari, M. Darus and U. S. Kirmaci, Refinements of Hadamardtype inequalities for quasiconvex functions with applications to trapezoidal formula and to special means, Comput. Math. Appl., 59 (2010), 225232. 

3 
S. S. Dragomir, Two mappings associated with Jensen's inequality, Extracta Math., 8 (1993), 102105. 

4 
S. S. Dragomir and D. M. Milošević, Two mappings in connection to Jensen's inequality, Zb. Rad. (Krajujevac), 15 (1994), 6573. 

5 
S. S. Dragomir and D. M. Milošević, Two mappings in connection to Jensen's inequality, Math. Balkanica (N.S.), 9 (1995), 39. 

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), 19. 

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), 93100. 

8 
S. S. Dragomir and C. E. M. Pearce, Quasiconvex functions and Hadamard's inequality, Bull. Austral. Math. Soc., 57 (1998), 377385. 

9 
S. S. Dragomir, J. E. Pečarić and L. E. Persson, Some inequalities of Hadamard type, Soochow J. Math., 21 (1995), 335341. 

10 
A. Eberhard and C. E. M. Pearce, Classinclusion properties for convex functions, in "Progress in Optimization" (Perth 1998), Appl. Optim., Kluwer Acad. Publ., Dordrecht, 39 (2000), 129133. 

11 
N. Hadjisavvas, Hadamardtype inequalities for quasiconvex functions, J. Inequal. Pure Appl. Math., 4 (2003), 6 pp. (electronic). 

12 
D. A. Ion, Some estimates on the HermiteHadamard inequality through quasiconvex functions, An. Univ. Craiova Ser. Mat. Inform., 34 (2007), 8388. 

13 
M. Jovanović, Some inequalities for strong quasiconvex functions, Glas. Mat. Ser. III, 24 (1989), 2529. 

14 
M. Merkle, Jensen's inequality for multivariate medians, J. Math. Anal. Appl., 370 (2010), 258269. 

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), 403409. 

16 
C. E. M. Pearce and A. M. Rubinov, $P$functions, quasiconvex functions and Hadamardtype inequalities, J. Math. Anal. Applic., 240 (1999), 92104. 

17 
A. M. Rubinov and J. Dutta, Hadamard type inequality for quasiconvex functions in higher dimensions, J. Math. Anal. Appl., 270 (2002), 8091. 

18 
M. Wagner, Jensen's inequality for the lower semicontinuous quasiconvex envelope and relaxation of multidimensional control problems, J. Math. Anal. Appl., 355 (2009), 606619. 

Go to top
