### Abstract

Hermite-Hadamard inequality is an important integral inequality in mathematics giving upper and lower bounds for the integral average of convex (concave) functions defined on closed intervals. Sandor’s inequality is the same Hermite-Hadamard inequality but for the square of convex (concave) functions. In this paper, Sandor’s inequality for nonlinear Sugeno integral is proved, i.e. some optimal bounds for the Sugeno integral of the square of concave functions are given. To illustrate the results, some examples with their geometric interpretations are presented.

Original language | English |
---|---|

Pages (from-to) | 13-28 |

Number of pages | 16 |

Journal | Advances in Nonlinear Variational Inequalities |

Volume | 20 |

Issue number | 2 |

Publication status | Published - Jul 1 2017 |

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### Keywords

- Hermite-Hadamard inequality
- Non-additive measure
- Sandor inequality
- Sugeno integral

### ASJC Scopus subject areas

- Analysis

### Cite this

*Advances in Nonlinear Variational Inequalities*,

*20*(2), 13-28.

**Estimation Bounds for Nonlinear Integral of the Square of Concave Functions.** / Abbaszadeh, Sadegh; Eshaghi, Madjid; Pap, E.; Ebadian, Ali.

Research output: Contribution to journal › Article

*Advances in Nonlinear Variational Inequalities*, vol. 20, no. 2, pp. 13-28.

}

TY - JOUR

T1 - Estimation Bounds for Nonlinear Integral of the Square of Concave Functions

AU - Abbaszadeh, Sadegh

AU - Eshaghi, Madjid

AU - Pap, E.

AU - Ebadian, Ali

PY - 2017/7/1

Y1 - 2017/7/1

N2 - Hermite-Hadamard inequality is an important integral inequality in mathematics giving upper and lower bounds for the integral average of convex (concave) functions defined on closed intervals. Sandor’s inequality is the same Hermite-Hadamard inequality but for the square of convex (concave) functions. In this paper, Sandor’s inequality for nonlinear Sugeno integral is proved, i.e. some optimal bounds for the Sugeno integral of the square of concave functions are given. To illustrate the results, some examples with their geometric interpretations are presented.

AB - Hermite-Hadamard inequality is an important integral inequality in mathematics giving upper and lower bounds for the integral average of convex (concave) functions defined on closed intervals. Sandor’s inequality is the same Hermite-Hadamard inequality but for the square of convex (concave) functions. In this paper, Sandor’s inequality for nonlinear Sugeno integral is proved, i.e. some optimal bounds for the Sugeno integral of the square of concave functions are given. To illustrate the results, some examples with their geometric interpretations are presented.

KW - Hermite-Hadamard inequality

KW - Non-additive measure

KW - Sandor inequality

KW - Sugeno integral

UR - http://www.scopus.com/inward/record.url?scp=85041215596&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85041215596&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:85041215596

VL - 20

SP - 13

EP - 28

JO - Advances in Nonlinear Variational Inequalities

JF - Advances in Nonlinear Variational Inequalities

SN - 1092-910X

IS - 2

ER -