Hermite-Hadamard type inequalities for subadditive functions

Huriye Kadakal; Huriye Kadakal

doi:10.3934/math.2020064

AIMS Mathematics

2020, Volume 5, Issue 2: 930-939. doi: 10.3934/math.2020064

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Research article

Hermite-Hadamard type inequalities for subadditive functions

Huriye Kadakal ^,

Ministry of Education, Giresun Hamdi Bozbağ Anatolian High School, Giresun-Turkey

Received: 06 November 2019 Accepted: 03 January 2020 Published: 08 January 2020
MSC : 26A51, 26D10, 26D15

In this paper, we will consider subadditive functions that take an important place not only in mathematics but also in physics and many other fields of science. Subadditive functions are very important also in economics and, specifically, in financial mathematics where subadditive discount functions describe certain behaviors in intertemporal choice and its anomalies. For example, some properties and characterizations of subadditive discount functions can be found in [11]. We establish Hermite-Hadamard-like inequalities for subadditive functions. Moreover, by using an integral identity together with some well known integral inequalities, we obtain several new inequalities for subadditive functions. Moreover, using subadditive functions we give some examples for the Hermite-Hadamard type inequalities. Some applications to special means of real numbers are also given. Especially, it should be noted that the results obtained in this paper coincide with previously obtained results in the literature under certain conditions.
- subadditive function,
- Hermite-Hadamard inequality
Citation: Huriye Kadakal. Hermite-Hadamard type inequalities for subadditive functions[J]. AIMS Mathematics, 2020, 5(2): 930-939. doi: 10.3934/math.2020064

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Abstract

In this paper, we will consider subadditive functions that take an important place not only in mathematics but also in physics and many other fields of science. Subadditive functions are very important also in economics and, specifically, in financial mathematics where subadditive discount functions describe certain behaviors in intertemporal choice and its anomalies. For example, some properties and characterizations of subadditive discount functions can be found in [11]. We establish Hermite-Hadamard-like inequalities for subadditive functions. Moreover, by using an integral identity together with some well known integral inequalities, we obtain several new inequalities for subadditive functions. Moreover, using subadditive functions we give some examples for the Hermite-Hadamard type inequalities. Some applications to special means of real numbers are also given. Especially, it should be noted that the results obtained in this paper coincide with previously obtained results in the literature under certain conditions.

References

[1]	A. O. Akdemir, M. E. Özdemir, F. Sevinç, Some inequalities for GG-convex functions, Turkish J. Ineq., 2 (2018), 78-86.
[2]	R. Bowen, Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms, Lecture Notes in Mathematics, Springer-Verlag, Berlin, 1975.
[3]	D. Ruelle, Ergodic theory of differentiable dynamical systems, Publications Mathématiques de l'Institut des Hautes Études Scientifiques, 50 (1979), 27-58.
[4]	S. S. Dragomir, R. P. Agarwal, Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula, Appl. Math. Lett., 11 (1998), 91-95.
[5]	V. Hutson, The stability under perturbations of repulsive sets, J. Differ. Equations, 76 (1988), 77-90. doi: 10.1016/0022-0396(88)90064-2
[6]	J. Hadamard, Etude sur les proprietes des fonctions entieres en particulier d'une fonction consideree par Riemann, J. Math. Pure. Appl., (1893), 171-216.
[7]	İ. İşcan, Ostrowski type inequalities for p-convex functions, New Trends in Mathematical Sciences, 4 (2016), 140-150. doi: 10.20852/ntmsci.2016318838
[8]	V. I. Oseledec, A multiplicative ergodic theorem. Ljapunov Characteristic Numbers for Dynamical Systems, Trans. Moscow Math. Soc., 19 (1968), 197-231.
[9]	S. Özcan and İ. İşcan, Some new Hermite-Hadamard type inequalities for s-convex functions and their applications, J. Inequal. Appl., 2019 (2019), 201.
[10]	S. Özcan, Some integral inequalities for harmonically (α, s)-convex functions, Journal of Function Spaces, 2019 (2019), 1-8.
[11]	S. C. Rambaud, S. Cruz and M. J. M. Torrecillas, Some characterizations of (strongly) subadditive discounting functions, Appl. Math. Comput., 243 (2014), 368-378.
[12]	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
[13]	J. Sándor, Generelizations of Lehman's inequality, Soochow Journal of Mathematics, 32 (2006), 301-309.
[14]	G. H. Toader, On generalization of the convexity, Mathematica, 30 (1988), 83-87.
[15]	M. J. Vivas-Cortez, R. Liko, A. Kashuri, et al. New Quantum sstimates of trapezium-type inequalities for generalized φ-convex functions, Mathematics, 7 (2019), 1047.

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