×

Some properties and inequalities for \(h\)-geometrically convex functions. (English) Zbl 1412.26024

Summary: In the paper, the definition of properties of \(h\)-geometrically convex functions are studied, and several integral inequality for the newly defined functions are established.

MSC:

26A51 Convexity of real functions in one variable, generalizations
26D15 Inequalities for sums, series and integrals
41A55 Approximate quadratures
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] R.-F. BAI, F. QI,ANDB.-Y. XI, Hermite-Hadamard type inequalities for the m - and(α,m)logarithmically convex functions, Filomat 27 (2013), no. 1, 1–7, available online at http://dx.doi.org/10.2298/FIL1301001B. · Zbl 1340.26043
[2] S.-P. BAI ANDF. QI, Some inequalities for(s1,m1)-(s2,m2)-convex functions on the co-ordinates, Glob. J. Math. Anal. 1 (2013), no. 1, 22–28.
[3] S.-P. BAI, S.-H. WANG,ANDF. QI, Some Hermite-Hadamard type inequalities for n -time differentiable(α,m)-convex functions, J. Inequal. Appl. 2012, 2012: 267, 11 pages, available online at http://dx.doi.org/10.1186/1029-242X-2012-267.
[4] M. E. ¨OZDEMIR, M. TUNC¸ ,ANDM. G ¨URBUZ¨, Definitions of h -logaritmic, h -geometric and h multi convex functions and some inequalities related to them, available online at http://arxiv.org/abs/1211.2750.
[5] Y. SHUANG, H.-P. YIN,ANDF. QI, Hermite-Hadamard type integral inequalities for geometricarithmetically s -convex functions, Analysis (Munich) 33 (2013), no. 2, 197–208, available online at http://dx.doi.org/10.1524/anly.2013.1192.
[6] S. VAROˇSANEC, On h -convexity, J. Math. Anal. Appl. 326 (2007), no. 1, 303–311, available online at http://dx.doi.org/10.1016/j.jmaa.2006.02.086.
[7] B.-Y. XI, R.-F. BAI,ANDF. QI, Hermite-Hadamard type inequalities for the m - and(α,m)geometrically convex functions, Aequationes Math. 184 (2012), no. 3, 261–269, available online at http://dx.doi.org/10.1007/s00010-011-0114-x. · Zbl 1264.26033
[8] B.-Y. XI ANDF. QI, Hermite-Hadamard type inequalities for functions whose derivatives are of convexities, Nonlinear Funct. Anal. Appl. 18 (2013), no. 2, 163–176. · Zbl 1293.26016
[9] B.-Y. XI ANDF. QI, Some Hermite-Hadamard type inequalities for differentiable convex functions and applications, Hacet. J. Math. Stat. 42 (2013), no. 3, 243–257. · Zbl 1292.26061
[10] B.-Y. XI ANDF. QI, Some inequalities of Hermite-Hadamard type for h -convex functions, Adv. Inequal. Appl. 2 (2013), no. 1, 1–15.
[11] B.-Y. XI, S.-H. WANG,ANDF. QI, Properties and inequalities for the h - and(h,m)-logarithmically convex functions, Creat. Math. Inform. (2013), no. 2, in press.
[12] B.-Y. XI, Y. WANG,ANDF. QI, Some integral inequalities of Hermite-Hadamard type for extended (s,m)-convex functions, Transylv. J. Math. Mechanics 5 (2013), no. 1, 69–84. · Zbl 1292.26062
[13] T.-Y. ZHANG, A.-P. JI,ANDF. QI, Integral inequalities of Hermite-Hadamard type for harmonically quasi-convex functions, Proc. Jangjeon Math. Soc. 16 (2013), no. 3, 399–407.
[14] T.-Y. ZHANG, A.-P. JI,ANDF. QI, On integral inequalities of Hermite-Hadamard type for s geometrically convex functions, Abstr. Appl. Anal. 2012 (2012), Article ID 560586, 14 pages, available online at http://dx.doi.org/10.1155/2012/560586.
[15] T.-Y. ZHANG, A.-P. JI,ANDF. QI, Some inequalities of Hermite-Hadamard type for GA-convex functions with applications to means, Matematiche (Catania) 68 (2013), no. 1, 229–239, available online at http://dx.doi.org/10.4418/2013.68.1.17. · Zbl 1281.26024
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.