Integral inequalities of Hermite-Hadamard type for exponentially subadditive functions

Serap Özcan; Serap Özcan

doi:10.3934/math.2020194

AIMS Mathematics

2020, Volume 5, Issue 4: 3002-3009. doi: 10.3934/math.2020194

Previous Article Next Article

Research article

Integral inequalities of Hermite-Hadamard type for exponentially subadditive functions

Serap Özcan ^,

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

Received: 03 December 2019 Accepted: 19 March 2020 Published: 20 March 2020
MSC : 26A51, 26D10, 26D15

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.
- subadditive function,
- exponentially subadditive function,
- Hermite-Hadamard inequalities
Citation: Serap Özcan. Integral inequalities of Hermite-Hadamard type for exponentially subadditive functions[J]. AIMS Mathematics, 2020, 5(4): 3002-3009. doi: 10.3934/math.2020194

Related Papers:

Abstract

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.

References

[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. doi: 10.1016/j.jksus.2016.09.007
[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. doi: 10.1016/0022-247X(86)90185-X
[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. doi: 10.1016/0022-0396(88)90064-2
[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. doi: 10.20852/ntmsci.2016216999
[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. doi: 10.1090/S0002-9939-1993-1176072-2
[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. doi: 10.18576/amis/120215
[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. doi: 10.1186/s13660-019-1955-4
[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. doi: 10.1016/S0893-9659(99)00164-0
[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. doi: 10.1007/s11253-015-1103-3
[17]	R. A. Rosenbaum, Sub-additive functions, Duke Math. J., 17 (1950), 227-247. doi: 10.1215/S0012-7094-50-01721-2
[18]	D. Ruelle, Ergodic theory of differentiable dynamic systems, Publ. Math. Paris, 50 (1979), 27-58. doi: 10.1007/BF02684768
[19]	M. B. Ruskai, Inequalities for quantum entropy: A review with conditions for equality, J. Math. Phys., 43 (2002), 4358-4375. doi: 10.1063/1.1497701
[20]	M. Z. Sarikaya, H. Budak, Generalized Hermite-Hadamard type integral inequalities for fractional integrals, Filomat, 30 (2016), 1315-1326. doi: 10.2298/FIL1605315S
[21]	M. Z. Sarikaya, M. A. Ali, Hermite-Hadamard type inequalities and related inequalities for subadditive functions, 2019, Available from: https://www.researchgate.net/publication/337022560.
[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.

Reader Comments

Your name:*

Email:*
© 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)