Fuzzy Ostrowski type inequalities via \(\phi\)-\(\lambda\)-convex functions

Volume 28, Issue 3, pp 224--235 http://dx.doi.org/10.22436/jmcs.028.03.02

Publication Date: June 26, 2022 Submission Date: August 22, 2021 Revision Date: December 13, 2021 Accteptance Date: March 18, 2022

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Authors

A. Hassan - Department of Mathematics, Shah Abdul Latif University, Khairpur-66020, Pakistan. A. R. Khan - Department of Mathematics, University of Karachi, University Road, Karachi-75270, Pakistan. F. Mehmood - Department of Mathematics, Dawood University of Engineering and Technology, M. A Jinnah Road, Karachi-74800, Pakistan. M. Khan - Department of Mathematics, Dawood University of Engineering and Technology, M. A Jinnah Road, Karachi-74800, Pakistan.

Abstract

We would like to state well-known Ostrowski inequality via \(\phi\)-\(\lambda\)-convex by using the Fuzzy Reimann integrals. In addition, we establish some Fuzzy Ostrowski type inequalities for the class of functions whose derivatives in absolute values at certain powers are \(\phi\)-\(\lambda\)-convex by Holder's and power mean inequalities. We are introducing very first time that the class of \(\phi\)-\(\lambda\)-convex function, which is the generalization of many important classes including class of \(h\)-convex, Godunova-Levin \(s\)-convex, \(s\)-convex in the \(2^{\rm nd}\) kind and hence contains convex functions. It also contains class of \(P\)-convex and class of Godunova-Levin. In this way we also capture the results with respect to convexity of functions.

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Keywords

• Ostrowski inequality
• convex functions
• fuzzy sets

MSC

•  26A33
•  26A51
•  26D15
•  26D99
•  47A30
•  33B10

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