IJPAM: Volume 118, No. 1 (2018)

Title

HERMITE-HADAMARD TYPE INEQUALITY FOR PRODUCT
OF CONVEX FUNCTIONS VIA SUGENO INTEGRALS

Authors

Deepak B. Pachpatte$^1$, Kavita U. Shinde$^2$
$^{1,2}$Department of Mathematics
Dr. Babasaheb Ambedkar Marathwada University
Aurangabad, 431 004 (M.S), INDIA

Abstract

The aim of this paper is to obtain, Hermite-Hadamard type inequality for product of convex function using Sugeno integral which is based on $(\alpha,m)$-convex function. Some application of our results are also given.

History

Received: 2017-02-07
Revised: 2017-12-19
Published: February 14, 2018

AMS Classification, Key Words

AMS Subject Classification: 03E72, 28B15, 28E10, 26D10
Key Words and Phrases: Hermite-Hadamard type inequality for product of convex function, Sugeno integrals, $(\alpha,m)$-convex function

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Bibliography

1
A. Flores-Franulic, H. Roman-Flores, A Chebyshev type inequality for fuzzy integrals, Appl. Math. comput., 190(2007), 1178-1184, doi: https://doi.org/10.1016/j.amc.2007.02.143.

2
A. Flores-Franulic, H. Roman-Flores, Y. Chalco-Cano, Markov type inequalities for fuzzy integrals, Appl. Math. Comput., 207(2009), 242-247, doi: https://doi.org/10.1016/j.amc.2008.10.029.

3
A. Flores-Franulic, H. Roman-Flores, Y.Chalco-Cano, A note on fuzzy integral inequality of Stolarsky type, Appl. Math. Comput., 196(2008), 55-59, doi: https://doi.org/10.1016/j.amc.2007.05.032.

4
B. G. Pachpatte, On some inequalities for convex functions, RGMIA Res. Rep. Coll. E, vol., 6(2003).

5
Dong-Qing Li, Yu-Hu Cheng, Xue-Song Wang and Shao-Fei Zang, Barnes-Godunova-Levin type inequalities of Sugeno integral for an $(\alpha,m)$-concave function. J. Inequ. Appl., (2015), doi: https://doi.org/10.1186/s13660-015-0556-0.

6
Dong-Qing Li, Xiao-Qiu Song, Tian Yue, Hermite-Hadamard type inequality for Sugeno integrals, Appl. Math. Comput., 237(2014), 632-638, doi: https://doi.org/10.1016/j.amc.2014.03.144.

7
D. Ralescu, G. Adams, The fuzzy integral, J. Math. Anal. Appl., 75(1980), 562-570, doi: https://doi.org/10.1016/0022-247$×$(80)90101-8.

8
H. Agahi, R. Mesiar, Y. Ouyang, E. Pap, M. Strooja, Berwald type inequality for Sugeno integral, Appl. Math. Comput., 217(2010), 4100-4108, doi: https://doi.org/10.1016/j.amc.2010.10.027.

9
H. Agahi, R. Mesiar, Y. Ouyang, General Minkowski type inequalities for Sugeno integral, Fuzzy Sets Syst., 161(2010), 708-715, doi: https://doi.org/10.1016/j.fss.2009.10.007.

10
H. Agahi, H. Roman-Flores, A. Flores-Franulic, General Barnes-Godunova-Levin type inequalities for Sugeno integral, Inf. Sci., 181(2011), 1072-1079, doi: https://doi.org/10.1016/j.ins.2010.11.029.

11
H. Roman-Flores, A. Flores-Franulic, Y. Chalco-Cano, The fuzzy integral for monotone function, Appl. Math. comput., 185(2007), 492-498, doi: https://doi.org/10.1016/j.amc.2006.07.066.

12
H. Roman-Flores, A. Flores-Franulic, Y. Chalco-Cano, A Jensen type inequality for fuzzy integrals Inform. Sci., 177(2007), 3192-3201, doi: https://doi.org/10.1016/j.ins.2007.02.006.

13
H. Roman-Flores, A. Flores-Franulic, Y. Chalco-Cano, A Hardy type ineqaulity for fuzzy integral. Appl. Math. Comput., 204(2008), 178-183, doi: https://doi.org/10.1016/j.amc.2008.06.027.

14
H. Roman-Flores, A. Flores-Franulic, Y. Chalco-Cano, A Convolution type inequality for fuzzy integrals, Appl. Math. Comput., 195(2008), 94-99, doi: https://doi.org/10.1016/j.amc.2007.04.072.

15
H. Roman-Flores, Y. Chalco-Cano, Sugeno integral and geometric inequalities, Int. J. Uncertainty, Fuzziness, Knowledge-Based Syst., 15(2007), 1-11.

16
J. Caballero, K. Sadarangani, A Cauchy-Schwarz type inequality for fuzzy integrals, Nonlinear Anal., 73(2010), 3329-3335, doi: https://doi.org/10.1016/j.na.2010.07.013.

17
J. Caballero, K. Sadarangani, Chebyshev type inequality for Sugeno integrals, Fuzzy Sets Syst., 161(2010), 1480-1487, doi: https://doi.org/10.1016/j.amc.2007.02.143.

18
J. Caballero, K. Sadarangani, Sandor's inequality for Sugeno integrals, Appl. Math. Comput., 218(2011), 1617-1622, doi: https://doi.org/10.1016/j.amc.2011.06.041.

19
J. Caballero, K. Sadarangani, Fritz-Carlson's inequality for fuzzy integrals, Comput. Math. Appl., 59(2010), 2763-2767, doi: https://doi.org/10.1016/j.camwa.2010.01.045.

20
J. Caballero, K. Sadarangani, Hermite-Hadamard inequality for fuzzy integrals, Appl. Math. Compute., 215(2009), 2134-2138, doi: https://doi.org/10.1016/j.amc.2009.08.006.

21
M. Sugeno, Theory of fuzzy integrals and its applications (Ph.D Thesis), Tokyo Institute of Technology, (1974).

22
R. Mesiar, Y. Ouyang, General Chebyshev type inequalities for Sugeno integrals, Fuzzy Sets. Syst., 160(2009), 58-64, doi: https://doi.org/10.1016/j.fss.2008.04.002.

23
V. G. Mihesan, A generalization of the convexity, in Seminar on Functional Equation Approximation and Convexity Romania, 1993.

24
Z. Wang, G. J. Klir, Generalized Measure Theory, Springer, New York, (2008).

25
Z. Wang, G. J. Klir, Fuzzy Measures Theory, Plenum press, New York, (1992).

How to Cite?

DOI: 10.12732/ijpam.v118i1.2 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2018
Volume: 118
Issue: 1
Pages: 9 - 29


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