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Bất đẳng thức tích phân loại Hermite-Hadamard cho các hàm có đạo hàm bậc ba lồi
Tóm tắt
Trong bài báo này, các tác giả thiết lập một số bất đẳng thức mới loại Hermite-Hadamard đối với các hàm mà đạo hàm bậc ba của chúng là lồi.
Từ khóa
#Hàm lồi #bất đẳng thức Hermite-Hadamard #đạo hàm bậc ba #bất đẳng thức tích phân.Tài liệu tham khảo
Dragomir SS: Two mappings on connection to Hadamard’s inequality. J. Math. Anal. Appl. 1992, 167(1):49–56. Available online at 10.1016/0022-247X(92)90233-4
Kirmaci US: Inequalities for differentiable mappings and applications to special means of real numbers to midpoint formula. Appl. Math. Comput. 2004, 147(1):137–146. Available online at 10.1016/S0096-3003(02)00657-4
Dragomir SS, Pečarić J, Persson L-E: Some inequalities of Hadamard type. Soochow J. Math. 1995, 21(3):335–341.
Alomari M, Hussain S: Two inequalities of Simpson type for quasi-convex functions and applications. Appl. Math. E-Notes 2011, 11: 110–117.
Hudzik H, Maligranda L: Some remarks on s -convex functions. Aequ. Math. 1994, 48(1):100–111. Available online at 10.1007/BF01837981
Chun L, Qi F: Integral inequalities of Hermite-Hadamard type for functions whose 3rd derivatives are s -convex. Appl. Math. 2012, 3(11):1680–1685. Available online at 10.4236/am.2012.311232
Bai R-F, Qi F, Xi B-Y: Hermite-Hadamard type inequalities for the m - and (α,m) -logarithmically convex functions. Filomat 2013, 27(1):1–7. Available online at 10.2298/FIL1301001B
Bai S-P, Qi F:Some inequalities for ( s 1 , m 1 ) - ( s 2 , m 2 ) -convex functions on the co-ordinates. Glob. J. Math. Anal. 2013, 1(1):22–28.
Bakula MK, Özdemir ME, Pečarić J: Hadamard type inequalities for m -convex and (α,m) -convex functions. J. Inequal. Pure Appl. Math. 2008., 9(4): Article ID 96. Available online at http://www.emis.de/journals/JIPAM/article1032.html
Kavurmaci, H, Avci, M, Özdemir, ME: New inequalities of Hermite-Hadamard type for convex functions with applications. Available online at arXiv:1006.1593. e-printatarXiv.org
Qi F, Wei Z-L, Yang Q: Generalizations and refinements of Hermite-Hadamard’s inequality. Rocky Mt. J. Math. 2005, 35(1):235–251. Available online at 10.1216/rmjm/1181069779
Shuang Y, Yin H-P, Qi F: Hermite-Hadamard type integral inequalities for geometric-arithmetically s -convex functions. Analysis 2013, 33(2):197–208. Available online at 10.1524/anly.2013.1192
Xi B-Y, Qi F: Some Hermite-Hadamard type inequalities for differentiable convex functions and applications. Hacet. J. Math. Stat. 2013, 42(3):243–257.
Xi B-Y, Qi F: Hermite-Hadamard type inequalities for functions whose derivatives are of convexities. Nonlinear Funct. Anal. Appl. 2013, 18(2):163–176.
Xi B-Y, Qi F: Some inequalities of Hermite-Hadamard type for h -convex functions. Adv. Inequal. Appl. 2013, 2(1):1–15.
Xi B-Y, Wang Y, Qi F:Some integral inequalities of Hermite-Hadamard type for extended (s,m) -convex functions. Transylv. J. Math. Mech. 2013, 5(1):69–84.
Zhang T-Y, Ji A-P, Qi F: Integral inequalities of Hermite-Hadamard type for harmonically quasi-convex functions. Proc. Jangjeon Math. Soc. 2013, 16(3):399–407.
Zhang T-Y, Ji A-P, Qi F: On integral inequalities of Hermite-Hadamard type for s -geometrically convex functions. Abstr. Appl. Anal. 2013., 2013: Article ID 560586. Available online at 10.1155/2012/560586
Zhang T-Y, Ji A-P, Qi F: Some inequalities of Hermite-Hadamard type for GA-convex functions with applications to means. Matematiche 2013, 68(1):229–239. Available online at 10.4418/2013.68.1.17
Dragomir SS, Pearce CEM RGMIA Monographs. In Selected Topics on Hermite-Hadamard Type Inequalities and Applications. Victoria University, Melbourne; 2000. Available online at http://rgmia.org/monographs/hermite_hadamard.html
Niculescu CP, Persson L-E: Convex functions and their applications. In CMS Books in Mathematics. Springer, Berlin; 2005.