Abstract
Integral inequality is an interesting mathematical model due to its wide and significant applications in mathematical analysis and fractional calculus. In the present research article, we obtain new inequalities of Simpson’s integral type based on theφ-convex andφ-quasiconvex functions in the second derivative sense. In the last sections, some applications on special functions are provided and shown via two figures to demonstrate the explanation of the readers.
Highlights
Integral inequality is a modern model of approximation theory that describes the growth rate of competing mathematical analysis. is model is used in various fields such as ordinary differential equations [1,2,3,4,5] and fractional calculus [6,7,8,9,10,11,12,13,14,15,16,17]
Among the several known inequalities, the most simple is Simpson’s type, which has been successfully applied in several models of ordinary differential equations [18,19,20,21,22,23,24,25,26,27,28,29] and fractional differential equations [30,31,32]
This paper deals with the notations of φ-convex and φ-quasiconvex functions which were introduced by Gordji et al [33] as follows
Summary
Integral inequality is a modern model of approximation theory that describes the growth rate of competing mathematical analysis. is model is used in various fields such as ordinary differential equations [1,2,3,4,5] and fractional calculus [6,7,8,9,10,11,12,13,14,15,16,17]. If the function F is neither four times differentiable nor is the fourth derivative F(4) bounded on (ξ1, ξ2), we cannot apply the classical Simpson quadrature formula. Let F: J ⟶ R be twice differentiable function on J such that F′′ ∈ L1[ξ1, ξ2], where ξ1, ξ2 ∈ J with ξ1 < ξ2, we have. This paper deals with the notations of φ-convex and φ-quasiconvex functions which were introduced by Gordji et al [33] as follows. We will give examples for the above definitions. E essential object of this study is to establish new Simpson’s integral inequalities for the φ-convex and φ-quasiconvex functions in the second derivative sense at certain powers
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
