What question did this study set out to answer?

To develop a new sharp Fejér trapezoidal type inequality without assuming convexity of the derivative, broadening its applicability.

June 18, 2026Open Access

Sharp Fejer Trapezoidal Type Inequalities

Key Points

To develop a new sharp Fejér trapezoidal type inequality without assuming convexity of the derivative, broadening its applicability.
Introduced a sharp Fejér trapezoidal inequality utilizing absolute continuity and Grüss type inequalities.
Explored special cases including Riemann-Liouville fractional integrals and Hermite-Hadamard inequalities.
Analyzed applications to trigonometric functions and classical functions like Euler's beta and gamma functions.
Established a new inequality that applies beyond traditional convexity assumptions.
Demonstrated sharp inequalities related to fractional integrals and trapezoidal formulas.
Provided examples showcasing the new inequalities in action with trigonometric and special functions.

Abstract

This paper presents a new sharp Fejér trapezoidal type inequality, utilizing the concepts of absolute continuity, Chebyshev functionals, Grüss type inequalities, and some properties of the integral function ℳ defined on the interval r, s.Unlike classic versions, the absolute value of the derivative of the considered function is not assumed to be convex, a setting that broadens the applicability of the results.Additionally, several special cases, such as sharp inequalities related to Riemann-Liouville fractional integrals, sharp Hermite-Hadamard trapezoidal type inequalities, and trapezoidal formulas for the approximation of definite integrals are discussed, offering several examples and applications to trigonometric functions and Euler's beta and gamma functions.

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Sharp Fejer Trapezoidal Type Inequalities

Key Points

Abstract

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