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.
M. Rostamian Delavar (Mon,) studied this question.