New Bounds of Hadamard’s and Simpson’s Inequalities Involving Green Functions

Muhammad Zakria Javed, Awais Ali, Muhammad Uzair Awan, Lorentz Jäntschi () and Omar Mutab Alsalami
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Muhammad Zakria Javed: Department of Mathematics, Government College University Faisalabad, Faisalabad 38000, Pakistan
Awais Ali: Department of Mathematics, Government College University Faisalabad, Faisalabad 38000, Pakistan
Muhammad Uzair Awan: Department of Mathematics, Government College University Faisalabad, Faisalabad 38000, Pakistan
Lorentz Jäntschi: Department of Physics and Chemistry, Technical University of Cluj-Napoca, 400641 Cluj-Napoca, Romania
Omar Mutab Alsalami: Department of Electrical Engineering, College of Engineering, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia

Mathematics, 2025, vol. 13, issue 17, 1-23

Abstract: This manuscript aims to assess some new refinements of right Hadamard’s and Simpson’s-like inequalities by bridging the concepts of Green function theory and convexity framework. It is a known fact that Green functions are convex and symmetric. By considering the identities based on Green functions for second-order differentiable functions and elementary results of inequalities, convexity and bounded variation of functions, we present various new upper estimates of trapezoidal and Simpson’s inequalities. Also, the accuracy of the results is determined by illustrative numerical examples and simulations. Lastly, we furnish some novel applications to linear combinations of means and composite error estimates.

Keywords: convex function; green function; Hermite-Hadamard’s inequality; trapezoidal’s inequality; simpson’s inequality; applications (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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