Estimation Bounds for Nonlinear Integral of the Square of Concave Functions

Sadegh Abbaszadeh, Madjid Eshaghi, E. Pap, Ali Ebadian

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)13-28
Number of pages16
JournalAdvances in Nonlinear Variational Inequalities
Volume20
Issue number2
Publication statusPublished - Jul 1 2017

Fingerprint

Concave function
Hermite-Hadamard Inequality
Sugeno Integral
Convex function
Closed interval
Optimal Bound
Integral Inequality
Upper and Lower Bounds

Keywords

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

ASJC Scopus subject areas

  • Analysis

Cite this

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

In: Advances in Nonlinear Variational Inequalities, Vol. 20, No. 2, 01.07.2017, p. 13-28.

Research output: Contribution to journalArticle

Abbaszadeh, Sadegh ; Eshaghi, Madjid ; Pap, E. ; Ebadian, Ali. / Estimation Bounds for Nonlinear Integral of the Square of Concave Functions. In: Advances in Nonlinear Variational Inequalities. 2017 ; Vol. 20, No. 2. pp. 13-28.
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