Abstract
Based on the Riemann–Liouville fractional integral, a new form of generalized Simpson-type inequalities in terms of the first derivative is discussed. Here, some more inequalities for convexity as well as concavity are established. We expect that present outcomes are the generalization of already obtained results. Applications to beta, q-digamma, and Bessel functions are also provided.
Highlights
Integral inequalities have been widely used in various sciences, including mathematical sciences, applied sciences, differential equations, and functional analysis
In most mathematical analysis areas, many types of integral inequalities are used. ey are very important in approximation theory and numerical analysis, which estimate the error’s approximation [1,2,3]
Many scholars are interested in the Simpson-type inequality since it has been examined and studied for numerous classes of functions. Due to their efficacy and usefulness in pure and applied mathematics, Simpson-type and Newton-type results have been keenly interpolated for convex functions. e first striking result about the Simpson-type inequality along with its applications to the quadrature formula in numerical integration was given by Dragomir et al in [14]
Summary
Integral inequalities have been widely used in various sciences, including mathematical sciences, applied sciences, differential equations, and functional analysis. Ere are several important inequalities due to their direct applications in applied sciences (see [4,5,6,7,8]) Several integral inequalities, such as Holder’s inequality, Simpson’s inequality, Newton’s inequality, the Hermite–Hadamard inequality, Ostrowski’s inequality, Cauchy–Schwarz, and Chebyshev, are well known in classical analysis and have been proven and applied in the setup of q-calculus using classical convexity [9,10,11,12]. Many scholars are interested in the Simpson-type inequality since it has been examined and studied for numerous classes of functions. Due to their efficacy and usefulness in pure and applied mathematics, Simpson-type and Newton-type results have been keenly interpolated for convex functions.
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.
