Uncertain Hermite-Hadamard inequality for functions with (s,m)-Godunova-Levin derivatives via fractional integral

Volume 9, Issue 5, pp 3333--3347 http://dx.doi.org/10.22436/jnsa.009.05.119

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Authors

Ladan Avazpour - Department of Mathematics, Yasooj Branch, Islamic Azad University, Yasooj, Iran. Tofigh Allahviranloo - Department of Mathematics, Tehran Science and Research Branch, Islamic Azad University, Tehran, Iran. - Department of Mathematics and Statistics, University of Prince Edward Island, 550 University Ave, Charlottetown, PE, C1A 4P3, Canada. Shafiqul Islam - Department of Mathematics and Statistics, University of Prince Edward Island, 550 University Ave, Charlottetown, PE, C1A 4P3, Canada.

Abstract

In this paper, we mix both concepts of s-Godunova-Levin and m-convexity and introduce the (s,m)- Godunova-Levin functions. We introduce the fuzzy Hermite-Hadamard inequality for (s,m)-Godunova-Levin functions via fractional integral. Holder inequality is used for new bounds for fuzzy Hermite-Hadamard inequality. Then we accommodate this result with the previous works that have been done before.

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Keywords

• Fuzzy number
• fuzzy Hermite-Hadamard inequality
• s-Godunova-Levin function
• m-convex function
• fractional integral.

MSC

•  03E72
•  26A33
•  26D10

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