Ostrowski like inequalities for \((\alpha,\beta,\gamma,\delta)\)-convex functions via fuzzy Riemann integrals
Volume 31, Issue 2, pp 137--149
http://dx.doi.org/10.22436/jmcs.031.02.02
Publication Date: April 26, 2023
Submission Date: December 31, 2022
Revision Date: February 20, 2023
Accteptance Date: February 22, 2023
Authors
F. Mehmood
- Department of Mathematics, Samarkand State University, Samarkand 140104, Uzbekistan.
- Department of Mathematics, Dawood University of Engineering and Technology, Karachi-74800, Pakistan.
A. Hassan
- Department of Mathematics , Shah Abdul Latif University Khairpur, Pakistan .
A. Idrees
- Department of Basic Sciences, DHA Suffa University, Karachi-75500, Pakistan.
F. Nawaz
- Department of Mathematics , Dawood University of Engineering and Technology, Karachi-74800, Pakistan.
Abstract
In this paper, we present first time the generalised notion of \((\alpha,\beta,\gamma,\delta)\)-convex (concave) functions in mixed kind, which is the generalisation of functions: convex (concave), \(P\)-convex (concave), quasi-convex (concave), \(s\)-convex (concave) in \(1^{\rm st}\) kind, \(s\)-convex (concave) in \(2^{\rm nd}\) kind, \((s,r)\)-convex (concave) in mixed kind, \((\alpha,\beta)\)-convex (concave) in \(1^{\rm st}\) kind, \((\alpha,\beta)\)-convex (concave) in \(2^{\rm nd}\) kind. Our aim is to establish Ostrowski like inequalities via fuzzy Riemann integrals for \((\alpha,\beta,\gamma,\delta)\)-convex functions in mixed kind by applying several techniques involving power mean inequality and Hölder's inequality. Moreover, we would obtain various consequences with respect to the convexity of function as corollaries and remarks.
Share and Cite
ISRP Style
F. Mehmood, A. Hassan, A. Idrees, F. Nawaz, Ostrowski like inequalities for \((\alpha,\beta,\gamma,\delta)\)-convex functions via fuzzy Riemann integrals, Journal of Mathematics and Computer Science, 31 (2023), no. 2, 137--149
AMA Style
Mehmood F., Hassan A., Idrees A., Nawaz F., Ostrowski like inequalities for \((\alpha,\beta,\gamma,\delta)\)-convex functions via fuzzy Riemann integrals. J Math Comput SCI-JM. (2023); 31(2):137--149
Chicago/Turabian Style
Mehmood, F., Hassan, A., Idrees, A., Nawaz, F.. "Ostrowski like inequalities for \((\alpha,\beta,\gamma,\delta)\)-convex functions via fuzzy Riemann integrals." Journal of Mathematics and Computer Science, 31, no. 2 (2023): 137--149
Keywords
- Ostrowski inequality
- convex functions
- fuzzy set
- power mean inequality
- Hölder's inequality
MSC
- 26A33
- 26A51
- 26D15
- 26D99
- 47A30
- 33B10
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