Conformable fractional Hermite-Hadamard type inequalities for product of two harmonic 𝑠-convex functions

Meftah, B.; Benssaad, M.; Kaidouchi, W.; Ghomrani, S.

doi:10.1090/proc/15396

Conformable fractional Hermite-Hadamard type inequalities for product of two harmonic $s$-convex functions
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by B. Meftah, M. Benssaad, W. Kaidouchi and S. Ghomrani PDF

Proc. Amer. Math. Soc. 149 (2021), 1495-1506 Request permission

Abstract:

In this paper, we establish some conformable fractional Hermite-Hadamard type integral inequalities via harmonic $s$-convexity, and the estimates of the products of two harmonic $s$-convex functions are also considered.

References

Thabet Abdeljawad, On conformable fractional calculus, J. Comput. Appl. Math. 279 (2015), 57–66. MR 3293309, DOI 10.1016/j.cam.2014.10.016
Muhammad Uzair Awan, Muhammad Aslam Noor, Marcela V. Mihai, and Khalida Inayat Noor, Inequalities via harmonic convex functions: conformable fractional calculus approach, J. Math. Inequal. 12 (2018), no. 1, 143–153. MR 3771790, DOI 10.7153/jmi-2018-12-11
Wolfgang W. Breckner, Stetigkeitsaussagen für eine Klasse verallgemeinerter konvexer Funktionen in topologischen linearen Räumen, Publ. Inst. Math. (Beograd) (N.S.) 23(37) (1978), 13–20 (German). MR 508122
F. Chen and S. Wu, Some Hermite-Hadamard type inequalities for harmonically $s$-convex functions. Scientific World J., 2014 (2014), Article ID 279158, 7 pages.
Sever S. Dragomir and Simon Fitzpatrick, The Hadamard inequalities for $s$-convex functions in the second sense, Demonstratio Math. 32 (1999), no. 4, 687–696. MR 1740330
İmdat İşcan, Hermite-Hadamard type inequalities for harmonically convex functions, Hacet. J. Math. Stat. 43 (2014), no. 6, 935–942. MR 3331150
İmdat İşcan and Shanhe Wu, Hermite-Hadamard type inequalities for harmonically convex functions via fractional integrals, Appl. Math. Comput. 238 (2014), 237–244. MR 3209630, DOI 10.1016/j.amc.2014.04.020
Imdat Iscan, Ostrowski type inequalities for harmonically $s$-convex functions, Konuralp J. Math. 3 (2015), no. 1, 63–74. MR 3376554
Anatoly A. Kilbas, Hari M. Srivastava, and Juan J. Trujillo, Theory and applications of fractional differential equations, North-Holland Mathematics Studies, vol. 204, Elsevier Science B.V., Amsterdam, 2006. MR 2218073
U. S. Kirmaci, M. Klaričić Bakula, M. E. Özdemir, and J. Pečarić, Hadamard-type inequalities for $s$-convex functions, Appl. Math. Comput. 193 (2007), no. 1, 26–35. MR 2385762, DOI 10.1016/j.amc.2007.03.030
B. Meftah and M. Merad, Hermite-Hadamard type inequalities for functions whose $n^{th}$ order of derivatives are $s$-convex in the second sense. Revista De Matemáticas De la Universidad del Atlántico Páginas. 4 (2017), no. 2, 87–99.
B. G. Pachpatte, On some inequalities for convex functions, RGMIA Res. Rep. Coll, 6 (2003), no. 1, 1–9.
J. Park, Hermite-Hadamard inequalities for harmonically $s$ -convex functions. Int. J. Pure Appl. Math. 99 (2015), no. 1, 37-49.
Josip E. Pečarić, Frank Proschan, and Y. L. Tong, Convex functions, partial orderings, and statistical applications, Mathematics in Science and Engineering, vol. 187, Academic Press, Inc., Boston, MA, 1992. MR 1162312
M. Z. Sarıkaya, E. Set, H. Yaldız, and N. Başak, Hermite-Hadamard’s inequalities for fractional integrals and related fractional inequalities, Mathematical and Computer Modelling, 57 (2013), 2403–2407.
E. Set, M. Z. Sarikaya, M. E. Özdemir, and H. Yildirim, The Hermite-Hadamard’s inequality for some convex functions via fractional integrals and related results, J. Appl. Math. Stat. Inform. 10 (2014), no. 2, 69–83. MR 3305933, DOI 10.2478/jamsi-2014-0014
Erhan Set, Ahmet Ocak Akdemir, and İ. Mumcu, Hadamard’s inequality and its extensions for conformable fractional integrals of any order $\alpha >0$, Creat. Math. Inform. 27 (2018), no. 2, 197–206. MR 3885365, DOI 10.37193/CMI.2018.02.12
Erhan Set and Abdurrahman Gözpınar, A study on Hermite-Hadamard type inequalities for $s$-convex functions via conformable fractional integrals, Stud. Univ. Babeş-Bolyai Math. 62 (2017), no. 3, 309–323. MR 3714103, DOI 10.24193/subbmath.2017.3.04
Erhan Set, Muhammed Aslam Noor, Muhammed Uzair Awan, and Abdurrahman Gözpinar, Generalized Hermite-Hadamard type inequalities involving fractional integral operators, J. Inequal. Appl. , posted on (2017), Paper No. 169, 10. MR 3673730, DOI 10.1186/s13660-017-1444-6
Erhan Set, Junesang Choi, and Abdurrahman Gözpinar, Hermite-Hadamard type inequalities for the generalized k-fractional integral operators, J. Inequal. Appl. , posted on (2017), Paper No. 206, 17. MR 3694985, DOI 10.1186/s13660-017-1476-y
Shu-Hong Wang and Feng Qi, Hermite-Hadamard type inequalities for $s$-convex functions via Riemann-Liouville fractional integrals, J. Comput. Anal. Appl. 22 (2017), no. 6, 1124–1134. MR 3644168