AIMS Mathematics, 2020, 5(4): 3002-3009. doi: 10.3934/math.2020194

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Integral inequalities of Hermite-Hadamard type for exponentially subadditive functions

Department of Mathematics, Kırklareli University, 39100, Kırklareli, Turkey

In this paper, we introduce a new class of functions, which is called exponentially subadditive functions. We establish Hermite-Hadamard inequalities via exponentially subadditive functions. We also give some related inequalities according with Hermite-Hadamard inequalities. Results obtained in this paper can be viewed as generalization of previously known results.
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1. N. Alp, M. Z. Sarıkaya, M. Kunt, et al. q-Hermite Hadamard inequalities and quantum estimates for midpoint type inequalities via convex and quasi-convex functions, J. King Saud Univ. Sci., 30 (2018), 193-203.    

2. R. Bowen, Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms, SpringerVerlag, Berlin, 1975.

3. F. M. Dannan, Submultiplicative and subadditive functions and integral inequalities of BellmanBihari type, J. Math. Anal. Appl., 120 (1986), 631-646.    

4. S. S. Dragomir, C. E. M. Pearce, Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA Monographs, Victoria University, 2000.

5. E. Hille, R. S. Phillips, Functional analysis and semi-groups, Amer. Math. Soc. Colloq. Publ., 31 (1957), 163-179.

6. V. Hutson, The stability under perturbations of repulsive sets, J. Differ. Equations, 76 (1988), 77-90.    

7. İ. İşcan, S. Turhan, S. Maden, Some Hermite-Hadamard-Fejer type inequalities for harmonically convex functions via fractional integral, New Trends Math. Sci., 4 (2016), 1-10.

8. M. Kadakal, İ. İşcan, Inequalities of Hermite-Hadamard and Bullen type for AH-convex functions, Universal J. Math. Appl., 2 (2019), 152-158.

9. M. Kunt, İ. İşcan, Fractional Hermite-Hadamard-Fejer type inequalities for GA-convex functions, Turkish J. Inequal., 2 (2018), 1-20.

10. J. Matkowski, T. Swiatkowski, On subadditive functions, P. Am. Math. Soc., 119 (1993), 187-197.    

11. M. U. Awan, M. A. Noor, K. I. Noor, Hermite-Hadamard inequalities for exponentially convex functions, Appl. Math. Inform. Sci., 12 (2018), 405-409.    

12. V. I. Oseledec, A multiplicative ergodic theorem, Trans. Moscow Math. Soc., 19 (1968), 197-231.

13. S. Özcan, İ. İşcan, Some new Hermite-Hadamard type inequalities for s-convex functions and their applications, J. Inequal. Appl., 2019 (2019), 1-11.    

14. B. G. Pachpatte, On some inequalities for convex functions, RGMIA Res. Rep. Coll., 6 (2003), 1-9.

15. C. E. M. Pearce, J. Pecaric, Inequalities for differentiable mappings with application to special means and quadrature formulae, Appl. Math. Lett., 13 (2000), 51-55.

16. F. Qi, T. Y. Zhang, B. Y. Xi, Hermite-Hadamard type integral inequalities for functions whose first derivatives are convex, Ukrainian Math. J., 67 (2015), 625-640.    

17. R. A. Rosenbaum, Sub-additive functions, Duke Math. J., 17 (1950), 227-247.    

18. D. Ruelle, Ergodic theory of differentiable dynamic systems, Publ. Math. Paris, 50 (1979), 27-58.    

19. M. B. Ruskai, Inequalities for quantum entropy: A review with conditions for equality, J. Math. Phys., 43 (2002), 4358-4375.    

20. M. Z. Sarikaya, H. Budak, Generalized Hermite-Hadamard type integral inequalities for fractional integrals, Filomat, 30 (2016), 1315-1326.    

21. M. Z. Sarikaya, M. A. Ali, Hermite-Hadamard type inequalities and related inequalities for subadditive functions, 2019, Available from:

22. E. Set, M. E. Özdemir, M. Z. Sarıkaya, et al. Hermite-Hadamard type inequalities for (α, m)-convex functions via fractional integrals, Moroccan J. Pure Appl. Anal., 3 (2017), 15-21.

23. G. H. Toader, On generalization of the convexity, Mathematica, 30 (1988), 83-87.

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