Corrected Dual-Simpson-Type Inequalities for Differentiable Generalized Convex Functions on Fractal Set
Abdelghani Lakhdari, Wedad Saleh, Badreddine Meftah, Akhlad Iqbal
Abstract
The present paper provides several corrected dual-Simpson-type inequalities for functions whose local fractional derivatives are generalized convex. To that end, we derive a new local fractional integral identity as an auxiliary result. Using this new identity along with generalized Hölder’s inequality and generalized power mean inequality, we establish some new variants of fractal corrected dual-Simpson-type integral inequalities. Furthermore, some applications for error estimates of quadrature formulas as well as some special means involving arithmetic and p-logarithmic mean are offered to demonstrate the efficacy of our findings.
Topics & Concepts
MathematicsQuadrature (astronomy)Differentiable functionLogarithmConvex functionInequalityType (biology)Regular polygonDual (grammatical number)Pure mathematicsApplied mathematicsMathematical analysisGeometryLiteratureArtEngineeringBiologyEcologyElectrical engineeringMathematical Inequalities and ApplicationsIterative Methods for Nonlinear EquationsMathematical functions and polynomials